Over a certain time period, did the number of shares of stock in Ruth's

Over a certain time period, did the number of shares of stock in Ruth's portfolio increase?

1) Over the time period, the ratio of the number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolio increased.
2) Over the time period, the total number of shares of stock and bonds in Ruth's portfolio increased

(2) INSUFFICIENT:
S + B could increase a number of ways:
S increase, B increase,
S no change, B increase,
S decrease, B increase (more so),
etc.
Probably no need to pick numbers here, although you could if you wanted to verify.

(1) INSUFFICIENT: The best way to interpret this ratio is to rely on fraction property rules to simplify. Note that S and B are non-negative. If the positive value X increases, then 1/X decreases. So if S/(S + B) increased, then (S + B)/S decreased. (S + B)/S = 1 + B/S, so we can conclude that B/S decreased.

B/S could decrease a number of ways:
S increase, B decrease,
S no change, B decrease,
S decrease, B decrease (more so),
etc.

But, I have to admit that I might just pick some numbers to see what could happen.

Let’s say that S = 10 and B = 20 at the beginning, so our original S/(S + B) = 10/(10 + 20) = 10/30 = 1/3. It’s best to try to prove insufficiency, which means we should try to make this ratio increase by both increasing S and not increasing S.

The ratio could increase if we increase S:
S increases to 12, B stays at 20, so the new S/(S + B) = 12/(12 + 20) = 12/32 > 1/3.

The ratio could increase if we don’t increase S:
S stays at 10, B decreases to 2, so the new S/(S + B) = 10/(10 + 2) = 10/12 = 5/6 > 1/3.

S could either increase or not.

(1) and (2) SUFFICIENT: Note that in order for the fraction S/(S + B) to increase as its denominator (S + B) increased, the numerator S must have increased, too.

One gram of a certain health food contains 7 percent of the minimum daily requirement of vitamin E and 3 percent of the minimum daily requirement of vitamin A. If vitamins E and A are to be obtained from no other source, approximately how many grams of the health food must be eaten daily to provide at least the minimum daily requirement of both vitamins?

A. 3
B. 7
C. 10
D. 14
E. 33

Given :  0.07 e + 0.03 a  = 1gm.

Now the least gm to achive the minimum daily requirement of the vitamins can be obtained by increasing Vitamin A to its minimum level of requirement:

i.e. 1 gm of the health food contains ------  ‘0.03*A’ gm of Vit A

So to ensure that minimum req of Vit A is covered we need cover how many gm of health food is required to raise this level to ‘A’ gm

i.e. To cover ‘A’ gm of Vit A  - A/0.03A = 33.33 gm

This many gms of heath-food ensures that it covers the minimum requirement of Vit A and also that of Vit E(actually Vit E would contain additional gms but we don’t care as covering 33.33 gm of the health food ensures that it covers the requirement of both Vit A & E and not of an individual component alone.)

Analogy :

let's say that granola bars come in bulk packs of 7 chocolate chip and 3 oatmeal raisin, and that you can't buy the flavors separately.

you need 100 chocolate chip and 100 oatmeal raisin bars for a catering event.

how many bulk packs do you have to buy?

same deal - you have to buy enough bulk packs to get 100 of BOTH kinds, which means you have to buy 33 1/3 of them (i.e., buy 34 of them) to get enough of the oatmeal raisin kind.
true, you'll have a whole lot of chocolate chip bars just sitting around, but that is irrelevant.

Are positive integers P and Q both greater than N?

Are positive integers P and Q both greater than N?

(1) P-Q is greater than N
(2) Q>P

Using Stmt 1)

P – Q >  N….we can infer P > N, but we have no info on Q. Can Q be less than N ?

Ex

P            Q               N

5            1                2

5            3                1

Insuff.

Using Stmt 2)

Q>P

But does no provide any information on N.

Insuff

Together :

Q > P > N….. Suff.

takeaway:
you can ADD TWO INEQUALITIES TOGETHER if the inequalities are BOTH "<" OR BOTH ">".

-q>n-p
+
q>p
_________
0>n

In 1995 Division A of Company X had 4850 customers. if there were 86 service errors

In 1995 Division A of Company X had 4850 customers. if there were 86 service errors in Division A that year, what was the service-error rate, in number of service errors per 100 customers, for Division B of company X in 1995 ?
(1) In 1995, the overall service-error rate for Divisions A and B combined was 1.5 service errors per 100 customers
(2) In 1995 Division B had 9350 customers, none of whom were customers of Division A

 From Statement (1)

(86 + x ) / (4850 + B) = 1.5 / 100

Where x = errors in Division B, B = customers in B.

Not Sufficient.

Is the above equation right?

From Statement (2)

We get B. Not Sufficient.

(1) + (2)

x is the only unknown. We can find x and later service errors per 100 customers.

If n is an integer, and r is the remainder when 4n+7 is

If n is an integer, and r is the remainder when 4n+7 is divided by 3, what is the value of r?

1) (n+1) is divisible by 3
2) n>20

statement 2 is probably easier to start with, since it doesn't have any glitz, glitter, or randomness; it's just a straight inequality. n is greater than 20.
there's not much to work with here, theory-wise, so let's just start plugging in some numbers.
n = 21 --> 4n + 7 = 91 --> remainder = 1 upon division by 3
n = 22 --> 4n + 7 = 95 --> remainder = 2 upon division by 3
insufficient.

--

statement 1:

easier method: JUST PLUG IN NUMBERS
it's not hard to generate plug-ins for this problem: just pick different multiples of 3 to stand in for (n + 1).
n + 1 = 3 --> n = 2 --> 4n + 7 = 15 --> remainder = 0 upon division by 3
n + 1 = 6 --> n = 5 --> 4n + 7 = 27 --> remainder = 0 upon division by 3
n + 1 = 9 --> n = 8 --> 4n + 7 = 39 --> remainder = 0 upon division by 3
n + 1 = 12 --> n = 11 --> 4n + 7 = 51 --> remainder = 0 upon division by 3
there's a clear pattern here: the remainder is always 0.
sufficient.

theory method #1:
you know that n + 1 is a multilple of 3. therefore, you can write n + 1 = 3k, where k is an integer.
subtract to isolate n --> n = 3k - 1.
therefore,
4n + 7
= 4(3k - 1) + 7
= 12k - 4 + 7
= 12k + 3
= 3(4k + 1)
= 3(integer)
therefore, (4n + 7) is a multiple of three. this means it will always yield a remainder of 0 upon division by three.

theory method #2:
instead of isolating n, factor as many (n + 1)'s as possible out of the given quantity.
4n + 7
= (4n + 4) + 3
= 4(n + 1) + 3
= 4(multiple of 3) + 3
= sum of 2 multiples of 3, since 4(multiple of 3) and 3 itself are both multiples of 3
= another multiple of 3
therefore, (4n + 7) is a multiple of three. this means it will always yield a remainder of 0 upon division by three.

ans = (a)

For any positive integer n, the length of n is defined as the number of prime factors

For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 x5x5. How many two digit positive integers have length 6?

A)None

B)One

C)Two

D)Three

E)Four

Smallest Number can be – 2^6.

Next highest number – 2^5 * 3

Next highest             - 2^4 * 3^2……. Not possible as it’s a 3 digit number….

Ans : C

What is the remainder when X^4 + Y^4 divide by 5

What is the remainder when X^4 + Y^4 divide by 5

A) X-Y divided by 5 gives remainder 1
B) X+Y divided by 5 gives remainder 2

Is Z an integer?

Is Z an integer?
A) Z^3 is an integer
B) 3Z is an integer

statement (1)

all we know is that z^3 is AN INTEGER. in particular, we can't deduce that z^3 is a perfect cube.

if z^3 is a PERFECT CUBE, such as 1, 8, or 27, then z will be an integer.
if z^3 is NOT a perfect cube, such as 2, 3, 4, etc., then z will NOT be an integer.

therefore, INSUFFICIENT.

(notice that you can easily find this by PLUGGING IN NUMBERS. in fact, the very first two positive integers, 1 and 2, give "yes" and "no" respectively, so that's a clear "insufficient".)

if we assume that z^3 is a perfect cube, then we're assuming that z is an integer. if we make that (totally unfounded) assumption, then we shouldn't be surprised when we find a specious answer of "yes".

--

statement (2) is insufficient for exactly the reasons you have cited.

--

together is actually SUFFICIENT.

here's what i think is the easiest way to consider this:

* consider all the numbers that satisfy statement (2):
1/3, 2/3, 1, 4/3, 5/3, 2, etc.

* of these, the only ones that satisfy statement (1) as well are 1, 2, 3, ...
(all the fractional ones will still be fractions when you cube them)

* since these - the numbers that satisfy BOTH statements - are all integers, we have TOGETHER = SUFFICIENT.

answer = (c)

A child selected a three-digit number, XYZ, where X, Y, and Z denote the digits

A child selected a three-digit number, XYZ, where X, Y, and Z denote the digits of the number. If no two of the three digits were equal, what was the three-digit number?
(1) The sum of the digits was 10.
(2) X < Y < Z

I'd start w stmt B ..it's lot easier

X<Y<Z .. it can be anything .. 235, 236 ..etc
Not Suff

X+Y+Z = 10
many such numbers 109, 901 ..etc ...Not Suff

2 Stmts together

chose the hundred's digit to be really small maybe 1
then we can play w rest of the 2 digits .to get to 10
136 or 145 .....
Hence again not Suff..
Ans E

If x is an integer, is (x^2 + 1)(x+5) and even number

If x is an integer, is (x^2 + 1)(x+5) and even number?

1) x is an odd number
2) Each prime factor of x^2 is greater than 7

statement 2 is just being obnoxious; they're testing you to see whether you can decode this statement properly, and get down to the essence of what it's trying to tell you.

first of all, an important takeaway that seems to recur a lot:
POWERS of a number have EXACTLY THE SAME PRIME FACTORS as does the ORIGINAL NUMBER.
reason:
think about how you create powers: you just take a number, and multiply together multiple copies of the same number.
by so doing, you're just repeating the same prime factors, over and over and over again.

so, in this context, "prime factors of x^2" is the same as just "prime factors of x".

therefore,
(2) each prime factor of x is greater than 7

at this point, you should be thinking about even and odd, even though even/odd is not specifically addressed by statement 2.
you should be thinking about even/odd anyway, even though they are not mentioned in the statement, because the REST OF THE PROBLEM is clearly related to even/odd.

since ALL primes greater than 2 (and thus, a fortiori, all primes greater than 7) are odd, we have
each prime factor of x is odd
and therefore
x is odd.

this statement is therefore sufficient for the same reasons as is statement (1).

In a certain game, a large bag is filled with blue, green, purple and red chips worth

In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
1
2
3
4
5

break the number 88000 into prime factors..

1 x 2^6 X 5^3 X 11 = 88,000

after looking at factors we can say that purple ball comes from 2^6.
now check the posibility because it mentioned that purple chips are worth more than the green chips, but less than the red chips ( 5 < Purple ball < 11)

2^6 = 4^3 = 8^2 = 64

2, 4 and 64 rule out .. hence 8

if x plus y over z is equal to -2, is x positive

if x + y/ z is equal to -2, is x positive?

(1) z is negative
(2) y is positive

TAKEAWAY:
if a problem asks about a certain quantity or variable(s), then you should ISOLATE that quantity or variable(s).

this problem asks a question about x. therefore, you should isolate x.
if you do this, you get x = -y - 2z.

therefore, you have the rephrase you want:is (-y - 2z) positive?

(1)
insufficient, because we don't know anything about -y (which could be any number at all, and which could definitely be big enough to overwhelm -2z).

(2)
insufficient, because we don't know anything about -2z (which could be any number at all, and which could definitely be big enough to overwhelm -y).

(together)
-y must be negative, but could be ANY negative number.
-2z must be positive, but could be ANY positive number.
the desired sum is therefore (arbitrary pos #) + (arbitrary neg #), which could work out to any number at all.
insufficient.

ans (e)

a certain meter records voltage between 0 and 10 volts

a certain meter records voltage between 0 and 10 volts, inclusive. if the average value of 3 recordings from the meter was 8 volts, what was the smallest possible recording in volts?

A) 2
B) 3
C) 4
D) 5
E) 6

(v1+v2+v3)/3=8

v1+v2+v3=24

For any one to be min, the other two must be max. ****

max for v =10, If v1 is min and v2,v3 are max

v1= 24-20=4

Ans : C

****TAKEAWAY:

when you have numbers with a fixed sum or product:

if you want to MINIMIZE A QUANTITY, then you must MAXIMIZE ALL OTHER QUANTITIES in the sum or product.

if you want to MAXIMIZE A QUANTITY, then you must MINIMIZE ALL OTHER QUANTITIES in the sum or product.

If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the

If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile=5280 feet.
1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.








Q Stem:      
Is D '>' 6
I.e. S T '>' 6
S '>' 12 m/hr
S '>' 12 * 5280 / 60 * 60  ft/sec
(Convert the rate at the Q stem level itself so that you do don’t do any calculation in the actual problem)
i.e. S '>' 17.6 ft/sec?


I) S '>' 16 ft/sec
Insuff
II) S '<' 18 ft/sec
Insuff

Together – Insuff.

Ans : E

When N is divided by 10 the remainder is 1 and when

When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

1. 13
2. 3
3. 11
4. 6.
5. 17

TAKEAWAY:
to generate lists of NUMBERS THAT HAVE REMAINDER "R" UPON DIVISION BY "D":
just take MULTIPLES OF "D" and ADD "R" to them.

so:
numbers that have remainder = 1 upon division by 10:
1, 11, 21, 31, 41, 51, ...
numbers that have remainder = 2 upon division by 3:
2, 5, 8, 11, 14, 17, ...

you don't have to go very far (11) to find the first example.
the remainder when you divide 11 by 30 is 11**, so the answer is (c) 11.

What is the sum of all integers from 132 to 531, inclusive

What is the sum of all integers from 132 to 531, inclusive?

in this problem, you're looking for the SUM of a large SET OF NUMBERS.

when it comes to large SUMS, you should use the SUM FORMULA:
SUM = AVERAGE x NUMBER OF DATA POINTS

in this case, the NUMBER OF DATA POINTS is 400 (i.e., there are 500 integers being summed).
there are two ways to see this:
(1) use the "add one before you're done" rule (see the number properties guide):
number of integers = 531 - 132 + 1 = 532 - 132 = 400.
(2) if you subtract 131 from all of them, then 132, 133, 134, ..., 531 becomes 1, 2, 3, ..., 400. therefore, there are 400 integers. (this "matching technique" is only used for finding the NUMBER of integers in the list; obviously you can't do this when it comes to finding the average, or the sum, of the numbers.)

also, the AVERAGE is 331.5.
since this is a list of consecutive integers, you can just take the average of the first and last numbers, and that's the same as the average of the entire list.
this average is (132 + 531) / 2, or 331.5.

therefore, the sum is
400 x 331.5
= 132,600

If n[i] and m are positive integers, what is the remainder when

If n[i] and m are positive integers, what is the remainder when "3^(4n+2) + m" is divided by 10 ?

(1) n = 2
(2) m = 1

3^1 =3 ,3^2=9,3^3=27,3^4 =81,3^5 = 243
notice a pattern in the units digit? they repeat every fourth power. 3^1 & 3^5 have the same units digit,3^2 & 3 ^6 have the same units digit & so on
using (1)
9*3^4n + m becomes 9*3^8 + m
considering only units digit , 9*1 + m
INSUFFICENT
using (2)
9*3^4n + 1 , as shown above, for all values of n, units digit 3^4n remains the same. ( UD of 3^4=1,UD of 3^8 =1)
Now , considering only units digit
9*1 + 1 = 10 ,Hence B SUFFICIENT

The numbers x and y are not integers. the value of x is closest to which

The numbers x and y are not integers. the value of x is closest to which integer?
(1) 4 is the integer that is closest to x+y
(2) 1 is the integer that is closest to x-y










statement 1 means that 3.5 '<' x + y '<' 4.5
this of course doesn't tell us anything about the sizes of x and y.
for instance, x and y could be 1.5 and 2.5. or, they could be -999.5 and 1003.5.
insufficient by itself.
--
statement 2 means that 0.5 '<' x - y '<' 1.5
this likewise tells us nothing about the individual values of x and y.
for instance, x and y could be 2.5 and 1.5. or, they could be 1001.5 and 1000.5.
insufficient by itself.
--
together, you can ADD THE INEQUALITIES, so that 'y' cancels out.
(TAKEAWAY: you can add inequalities whenever the 'alligators' - i.e., the "'<'" or "'>'" - face the SAME WAY.)
this gives
3.5 '<' x + y '<' 4.5
0.5 '<' x - y '<' 1.5
add
4 '<' 2x '<' 6
therefore
2 '<' x '<' 3
this is still insufficient, because x could be closer to 2, closer to 3, or neither (if it's exactly in the middle, at 2.5).
ans (e).

if d is a positive integer and f is the product of the first 30 integers

if d is a positive integer and f is the product of the first 30 integers what is the value of d?

(1) 10^d is a factor of f
(2) d'>'6

here's all you have to do:
forget entirely about 10, 20, and 30, and ONLY THINK ABOUT PRIME FACTORIZATIONS.
(TAKEAWAY: this is the way to go in general - when you break something down into primes, you should not think in hybrid terms like this. instead, just translate everything into the language of primes.)

each PAIR OF A '5' AND A '2' in the prime factorization translates into a '10'.

there are seven 5's: one each from 5, 10, 15, 20, and 30, and two from 25.

there are way more than seven 2's.

therefore, 30! can accommodate as many as seven 10's before you run out of fives.

--

statement 2 is clearly insufficient.

statement 1, by itself, means that d can be anything from 1 to 7 inclusive.

together, d must be 7.

ans (c)

On the number line shown, is zero halfway between r and s

On the number line shown, is zero halfway between r and s?
<--r------s--t-->

1. s is to the right of zero
2. The distance between t and r is the same as the distance between t and –s

i would always think about these things SPATIALLY / VISUALLY at first, and set up algebraic equations only as a "plan b". the problem with algebraic equations is that it's too easy to fall into traps.

the particular trap you've fallen into in your interpretation of (2) is that of assuming "-s" is to the LEFT of "t". there is no good reason whatsoever to make this assumption, and, what's more, at least one good reason (viz., "the gmat loves to test exactly these sorts of assumptions) not to make it.
of course, you don't need reasons to be very careful about your assumptions; that should be your default state.

if "-s" is to the right of "t", then you have
<--r-------s---t-----------(-s)-->
in which case 0 is in no-man's-land between "t" and "-s".
in this case, note that "s" is negative. also note that (-s) is positive in this case, a situation that is difficult to digest for most students.

taking statements (1) and (2) together eliminates the above possibility, leaving only the case that you have outlined.

Ans C

Machine X and Y work at their respective constant rates. How many

Machine X and Y work at their respective constant rates. How many more hours does it take Machine Y, working alone, to fill a production order of a certain size than it takes Machine X, working alone?

1. Machine X and Y, working together, fill a production order of this size in two thirds the time that Machine X does.
2. Machine Y, working alone, fills a production order of this size in twice the time that Machine X, working alone, does.

Let x and y represent the respective rates of X and Y.
We must know the values of both x and y to know “how many more hours”. In other words, y = 2x does not tell us how many more hours the job takes Y than X, only that Y takes twice as long. If x = 2, y = 4 and the difference is 2. However, if x = 3, y = 6, and it now takes 3 hours longer.

1) 1/x + 1/y = 1/T
So, T (total time) = xy / (x+y)
Statement 1 tells us that the total time or combined = 2/3 x
So, xy / (x+y) = 2/3 x
Solve and you get y = 2x
INSUFFICIENT – again, it only gives us a relationship

2) translated gives y = 2x

Statements 1 and 2 provide the same information, so either D or E
Since we cannot combine 2 similar equations to solve for 2 variables, the answer is E

If √x is an integer, what is the value of √x

If √x is an integer, what is the value of √x?

1.) 11<x<17
2.) 2<√x<5

Given Data,
√x is an integer

Stmt 1:
11<x<17

so If √x is an integer, then fron (1) x = 16, so √x = 4 - SUFFICIENT

Stmt 2:
2<√x<5 here √x could be either 3 or 4. So INSUFFICIENT

If z^n = 1, what is the value of z?

If z^n = 1, what is the value of z?

1. n is a non zero integer.

2. z '>' 0. 

For z^n = 1, and n being a non zero integer, there are 3 possible ways.

a. 1^1 = 1

b. 1^- 1 = 1

c. - 1^2 = 1

Statement 1 not conclusive. Z could be 1 or -1.

Statement 2: z '>' 0.

==> we need both statements to solve for z.

Answer: C.

Connie Paid a sales tax of 8 percent on her purchase. If the sales

Connie Paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5%, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?

368
380
400
420
432

1) Solve for price:

P(.08)= (.05P)-12

P=400

2) add sales tax:

400(1.08) = 432

A and B working simultaneously can paint a Tank in 5/6 hrs. A and

A and B working simultaneously can paint a Tank in 5/6 hrs. A and C working simultaneously complete the same task in 3/2 hrs, while C and B working simultaneously complete it in 2 hrs. If A,B,and C were to work together how long would it take them to finish painiting the tank?

Now:

1/a + 1/b =   6/5

1/a + 1/c =   2/3

1/c + 1/b =   ½

1/a + 1/b + 1/c =   71/60

Total Hrs : 60/71

The table gives three factors to be considered when choosing

User-friendly 56%
Fast response time 48%
Bargain prices 42%

The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time”, what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”


A. 312
B. 336
C. 360
D. 384
E. 420

Now Total Correspondants – 100%

Hence….  100 = 56 + 48 + 42 – (30) – (Other associations of B…)

Other associations of B… = 16% = 0.16 * 1200 = 192

Now Overall Respondents of B = 0.42 * 1200 = 504.

 Only B Respondent’s = 504 – 192 = 312

Ans : A

If y and z are integers, is y(z + 1)

If y and z are integers, is y(z + 1) odd?

1. y is odd
2. z is even

Q Stem : IS y(z + 1) odd ?

Only when y – Odd and  Z+1 is Odd i.e. Z – Even, we can get the required.

Stmt 1) Insuff  as no info on Z

Stmt 1) Insuff as no info on Y

Together – Suff.

For a finite sequence of non zero numbers, the number of variations

For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1,-3,2,5,-4,-6?

1)1
2)2
3)3
4)4
5)5

(1,-3)  (-3,2) and (5,-4)

Ans :C

A certain car averages 25 miles per gallon when driving in the city

A certain car averages 25 miles per gallon when driving in the city and 40 miles to the gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and 50 miles on the highway?
 
a)28
b)30
c)33
d)36
e)38
 

Using weighted averages:

Avg Miles/ Gallon = 10 + 15 / (10/25  +  40/50)  = 60/(33/20) ~ 36.

Ans : d

In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If rest of the family's income did not change, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?

1. 64%
2. 68%
3. 72%
4. 76%
5. 80%

The Rest of the family income stay the same ,i.e = 100-60=40

Mrs Lee's Income increases by 20%=60+12=72

Therefore, Total Family earnings = Mrs Lee + Rest of the family=72+40=112

Percentage=(72/112)*100=63.7%=appr 64%

is 1/a-b ‘<’ b-a?

is 1/a-b ‘<’ b-a?

(1) a ‘<’ b

(2) 1 ‘<’ |a-b|

From a )

 a – b ‘<’ 0 i.e. a- b =  -ve

 b – a ‘>’ 0 i.e. b – a = + ve

Suff. 

From b)

If  a ‘>’ b ………a-b ‘>’ 1 &   b – a ‘<’  -1

If  a ‘<’ b ………a-b ‘>’ -1 &   b – a ‘<’  1

Depending on case we can have 2 possibilities’.

Hence Insuff.

Ans – A

On July 1 of last year, the total number of employees at Company E

On July 1 of last year, the total number of employees at Company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) empoloyee salary was 10 percent more after the decrease in number of employews than before the decrease. The total of the combine salaries of all the employees at Company E after July 1 last year was what percent of that before July 1 last year?

Possible answers

a. 90%
b. 99%
c. 100%
d. 101%
e. 110%

Avg  = Combined Sal / Emp Strength.

Let Comb Sal Before 1^st July = A * E

Now Comb Sal after 1^st July =  A*110/100  *    E*90/100

                                      = (99/100)  *A*E

                                      = (99/100)  * Comb Sal Before 1^st July

Ans : B

When positive integer n is divided by 3, the remainder is 2 and when

When positive integer n is divided by 3, the remainder is 2 and when positive integer t is divided by 5 the remainder is 3. What is the remainder when the product nt is divided by 15?

1. n-2 is divisible by 5
2. t is divisible by 3

Known from Q stem: n = 3k + 2; t = 5p + 3
Is this rephrasing correct? nt = 15kp + 9k + 10p + 6

Statement 1 tells us that:
(3k+2)-2 = an integer. (3k)/5. Thus, k must be a multiple of 5
5

Statement 2 tells us that:
5p+3 = an integer or (5/3)p +1 is an integer. Thus, p must be a multiple of 3
3

Going back to your original rephrase:
nt = 15kp + 9k + 10p + 6

rewrite as, what is the remainder of:
(15kp) + (3^2*k) + (2*5*p) + (6)
15

break down the four parts:
15kp/15 has no remainder
(3^2)*k/15 has no remainder because k is a multiple of 5
2*5*p/15 has no remainder because p is a multiple of 3
6 will always be the remainder and your answer is C

Number Plugging also works……….

The product of the units digit, the tens digit, and the hundreds

The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is the units digit of m?

(1) m is odd
(2) The hundreds digit of m is 8

Ans : A

If the drama club and music club are combined, what percent of

If the drama club and music club are combined, what percent of the combined membership will be male?

(1) of the 16 members of the drama club, 15 are male
(2) of the 20 members of the music club, 10 are male

one thing to note here is that you don't know the overlap, i.e the number of folks in the drama club, who are also members of the music club and vica versa.
Take this example,
20 members of the music club - 10 are male
all those 10 are also part of the drama club,
total ## of unique members: (16+ 20) - 10 = 26
## of males = 15
so % of males : 15/26 * 100

what if all members were exclusive, ie. no overlap
then % of males : 25/26 * 100

Therefore: E

Ans : E

How many people are directors of both charities A and B

How many people are directors of both charities A and B?

(1) Charity A has 16 directors and Charity B has 9 directors.

(2) 18 directors attended a joint meeting of the directors of Charity A and Charity B, and not one director was absent from the meeting.

COLUMNS: Charity A / NOT Charity A / Total

ROWS:
Charity B
NOT Charity B
Total

DESIRED QUANTITY is the TOP LEFT.

(a)
bottom left = 16
top right = 9
insufficient.

(b)
middle square = 0
bottom right = 18
insufficient.

(together)
if you have both statements, you can fill in the whole grid.
7 2 9
9 0 9
16 2 18
so, top left = 7.
sufficient.

Ans : C

Company C has a machine that, working alone at its constant rate

Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours. If Company C plans to buy a new machine that will process this product at a constant rate and if the two machines, working together at their respective constant rates, are to process 100 units of this product in 2 hours, what should be the constant rate, in units per hour, of the new machine?

A. 50
B. 45
C. 30
D. 25
E. 20

Let new machine produces ‘X’ Units in 1 hr.

In 1 hr A produces – 20 U

Together it produces 50 U in 1 hr.

Now 20 + X = 50

X = 30

Ans C

A certain kennel will house 24 dogs for 7 days. Each dog requires 10 ounces of dog food per day. If the kennel purchases dog food in cases of 30 cans each and if each can holds 8 ounces of dog food, how many cases will the kennel need to feed all of the dogs for 7 days?

A. 5
B. 6
C. 7
D. 8
E. 9

Total ounces of food required by 24 dogs for 7 days = 10*24*7 ------- (1)
Total ounces of dog food in each case = 30*8 ------------ (2)
Therefore, Total 1/Total 2 = 7. Answer is C.

Each year Mark works 40 hours per week for 50 weeks. Last year Mark

Each year Mark works 40 hours per week for 50 weeks. Last year Mark was paid a total of $20000. If this year his hourly pay rate is raised by $0.50, what is the total amount that Mark will be paid this year?

A. $30000
B. $25000
C. $22500
D. $21500
E. $20020

Total hours worked for 50 weeks = 50*40 = 2000 hours.
Hourly rate = 20000/2000 = $10/hr
New hourly rate = $10.50

Therefore, total amount that Mark will be paid this yr = 10.50 * 2000 = $21000.

Henry purchased 3 items during a sale. He received a 20 percent discount

Henry purchased 3 items during a sale. He received a 20 percent discount of the regular price of the most expensive item and a 10 percent discount off the regular price of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of regular prices of the 3 items?

1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20.
2) The regular price of the least expensive item was $15

From the question, Let I1 > I2, I3 where I1 is the most expensive item and I1 and I2 be the least expensive ones.

After, 20% off on I1 and 10% off on I2, I3, their prices reduce to .8I1, .9I2 and .9I3 respectively

Now converting the wording in the question to mathematical expression we need to find - >

.2I1 + .10I2 + .10I3 > .15(I1 + I2 +i3)

solving, we get I1 > I2 + I3 ( This is actually the question......we need to determine)

1) I1 =50 and I2 or I3 = 20, therefore if I2 or I3 =20 (the 2nd expensive one), the least expensive cannot be more than 20
so A answers the question...as YES

2) is insufficient as it only tells about one number.

on a certain tour, ratio of number of women to number of children was 10

on a certain tour, ratio of number of women to number of children was 10 to 4. what was the no of men on the tour?

(1) ratio of children to men was 10 to 22
(2) no of women on the tour was less than 30

Ratio of women (W) to children (C) is 10:4 or 5:2

(1) this only gives a ratio, and the prompt only provides a ratio.

W:C:M = 25:10:22.

With only ratios, there is no way to determine the actual # of men. INSUFFICIENT.

(2) this provides the actual number of women on the tour, but combined with the prompt provides no info on the # of men. INSUFFICIENT.

Together we find that if W<30 then the only condition that can be followed is that the number of W = 22. Hence number of M = 22

Ans C

Strategy for GMAT

1)     Micromanagement, which roughly means limiting yourself to APPROXIMATELY two minutes per problem.
this doesn't mean that you have to cut the rope at exactly two minutes; even in our 9-session course we acknowledge that there are certain problem types (most notably word translations and sometimes geometry) that routinely demand over 2 minutes even from very able students. conversely, there are also problem types (most notably fdp's) that should take substantially less than two minutes per problem. the idea is to get this to balance out.

2) macro-management, which means checking in on the timing guidelines periodically (= DO NOT stare at the lil timer in the corner of the screen after every single problem). this is where you figure out EVERY SO OFTEN whether you're in a hole, and whether you need to throw away questions.

(1) and (2) complement each other. DO NOT PRACTICE ONE OF THESE TWO FORMS OF TIME MANAGEMENT TO THE EXCLUSION OF THE OTHER ONE. in other words:
1) don't concentrate so much on spending exactly two minutes per problem that you wind up cutting off lots of productive solutions just because you're obsessed with the clock. this applies here; if you know you can nail this problem type in 2:30, then it's worthwhile to spend the extra :30 (as long as you don't find yourself in that situation more than a few times per test, AND you can solve other problem types fast enough to make up the deficit).
2) at the same time, don't completely neglect your per-problem timing responsibility. you don't want to wait until the next big checkpoint on your timing map (every 15 minutes or so) and suddenly discover that you're behind by 5 questions and you have no idea what happened.

Warehouse W's revenue from the sale of sofas was what percentage

Warehouse W's revenue from the sale of sofas was what percentage greater this year than it was last year?
1) Warehouse W sold 10% more sofas this year than last.
2) Warehouse W's selling price per sofa was $30 greater this year than last.

Ans : E.

The lifetimes of all the batteries produced by a certain company

The lifetimes of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean m. If the distribution has a standard deviation of d, what percent of the distribution is greater than m+d?

(1) 68 percent of the distribution lies in the interval from m-d to m+d, inclusive.
(2) 16 percent of the distribution is less than m-d.

The question stem tells you that Distribution is symmetrical around mean m so 50% above m and 50% below.

St-1 68% is between m-d and m+d, this tells you that on the side which is higher 34% is between m and m+d so, remaining 16% has to be above m+d. SUFFICIENT

St-2 tells you that 16% is below m-d, so on the other side 16% will be above m+d. SUFFICIENT as well.

This is actually a normal distribution, where 68% is between 1 Standard deviation (SD), 96% between 2 SD and rest within 3 SD.

Ans :D

Mark bought a set of 6 flower pots of different sizes at a total cost

Mark bought a set of 6 flower pots of different sizes at a total cost of 8.25. Each pot cost 0.25 more than the next one below in size. What is the cost of the largest pot?

8.25 = 6/2 (2*x + (6-1) * 0.25)

X = ¾

Now Largest Post price = ¾ + 1.25 = 2

Answer: $2.00

In a sample of college students, 40 percent are third-year students

In a sample of college students, 40 percent are third-year students and 70 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?

Use the double matrix as:

   Third Yr        No Third Yr

Second Yr     

No Second Yr

Ans : 30/60