In the graduating class of a certain college, 48% of the students are male and 52% are female

In the graduating class of a certain college, 48% of the students are male and 52% are female. In this class 40% of the male and 20% of the female students are 25years old or older. If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old??
A) 0.90
B) 0.70
C) 0.45
D) 0.30
E) 0.25 


 




This is really just a weighted average. We have two groups, men and women, and men have an 'average' of 40%, while women have an 'average' of 20%. The groups are almost equal in size, so when we combine them, the 'average' must be almost exactly 30%. So roughly 30% of all people are twenty-five years old or older, and roughly 70% are thus less than twenty-five, so the answer should be B.
--------------------------------------------------------------------------------------------------------
Whenever we have groups (in this case, male and female) that are being divided into smaller groups (in this case, those 25 and older and those less than 25), we can use a group grid to organize the data. Here's what the grid looks like:

_______________M______F_______Total

older:

younger:

total:

In the grid above, every row has to add up to the total, as does every column. Looking at the top row, older males + older females = total older. Looking at the left-most column, older males + younger males = total males.



Now let's fill in the data step by step. Let's plug in 100 for the total number of students:

_______________M______F_______Total

older:

younger:

total:__________________________100



48% males, 52% females. Since we're looking for an approximation, let's say that 50% are males and 50% are females:

_______________M______F_______Total

older:

younger:

total:__________50_____50________100



40% of the males and 20% of the females are 25 and older:

_______________M______F_______Total

older:__________20_____10_______

younger:

total:__________50_____50________100



Now we can complete the grid:

_______________M______F_______Total

older:__________20_____10________30

younger:_______30_____40________70

total:__________50_____50________100


Notice that everything adds up horizontally and vertically. Neat!

So P(younger) = 70/100 = .7

The correct answer is B.

 

Are x and y both positive?

Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1











For A) 2x - 2y = 1 -----> x - y = 1/2. You can have 0 - (-1/2) = No or You can have +1 - (+1/2) = Yes. So A is insufficient.

For B) x/y > 1 ---> Either X and Y are both + or X and Y are both negative. So B is insufficent. NOTE: |x| > |y|.

For A+B.

Have x and y be positive and make it work with equation A. So +1 - (+1/2) = 1/2 Yes.
.... be negative and make it work with equation B. So -1 - (-y) = 1/2. y = (3/2) which is > |x|. So you will see that two negatives cannot work because it violtates the rule that x/y > 1. So for A+B the answer is yes.

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

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.

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