After paying a 10% tax on all income over $3,000, a person had a

After paying a 10% tax on all income over $3,000, a person had a net income of $12,000.
What was the income before taxes?

A)$13,300
B) $13,000
C) $12,900
D) $10,000
E) $9,000













let the amt be x.... so 10% of(x-3000)is the tax.....
so x- (x-3000)*0.1=12000..
x=13000 

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.

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

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%

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

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.

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.

In May, Mrs. Lee’s earnings were 60%

In May, Mrs. Lee’s earnings were 60% of the Lee’s family Income. In June, Mrs. Lee earned 20% more than in May. If the rest of the family’s income was the same both months, then, in June, Mrs. Lee’s earnings were approximately what % of the Lee family’s total income?

a) 64%b) 68%c) 72%d) 76%e) 80%

Ans - A

How many liters of oil must be added to x liters of an oil-water solution that is y percent oil to produce a solution that is z percent oil?

Ans: l = xz-xy/100 -z

each of the students in a certain class received a single grade of P, F, or I. what percent of the students in the class were females?
1. of those who received a p, 40% were females
2. of those who received either an I or F, 80% were males.







one way you could do it: number picking. just try different numbers of P's and I's/F's, and see whether the answer is invariant or whether it changes. if it changes at all, then the data are insufficient.
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you could also do it by realizing that this is a WEIGHTED AVERAGE of 40% (the percentage of p's that are female) and 20% (the percentage of f/i's that are female). like any other weighted average, this one depends on the relative quantities of its components (here, p's versus f/i's), quantities that are not given in either of the two statements.
conceptually, if there are huge numbers of p's and negligible numbers of f/i's, then the percentage of females will be very close to 40%. conversely, if there are huge numbers of f/i's and very few p's, then the percentage will be very close to 20%.

in fact, there's nothing prohibiting the consideration of the two most extreme cases possible:
* ALL grades are p's --> 40% female
* ALL grades are f/i's --> 20% female
these situations are both allowed under the given conditions, so, insufficient.


Ans - E

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase



Ans - D

Amount Charged | Percent Bonus
$0.01 - $1000 | 0.5
$1000 - $3000 | 1.0
$3000 - $6000 | 1.5
$6000 - $10000 | 2.0


At the end of each year, a certain card company pays a bonus to each of its credit card holders based on the amount, up to $10,000, that the card holder charged throughout the year. A 0.5 percent bonus is paid on the first $1000 charged, a 1.0 percent bonus is paid on the next $2000 and so on, as indicated in the table above. What is the maximum annual bonus, in dollars?



The problem tells us that it will pay a bonus "up to $10,000" so if we want to know the maximum possible bonus, we have to assume the person charged $10,000.

For the first $1,000, the person earns a 0.5% bonus.
1000 = 100%
100 = 10%
10 = 1%
5 = 0.5%
So the person earns $5 for the first $1,000 charged.

For the next $2,000 charged (between $1,000 and $3,000), the person earns a 1% bonus.
200 = 10%
20 = 1%
So the person earns $20 for the next $2,000 charged. .......
.....

The Ans - 150

Jasons salary and Karens salary were each p percent greater in 1998 than in 1995 .What is the value of p ?

1) In 1995 Karens Salary was 2000 greater than Jasons
2) In 1998 Karens salary was 2440 greater than Jasons






OA - C

jack and mark both receive hourly wage increases of 6%. after the wage increase, jack's hourly wage was how many more dollars per hour than mark?

1. before the wage increases, jack's hourly rate was 5 more than mark's
2. before the wage increases, the ratio of jack's hourly wage to mark's hourly wage was 4 to 3



(1)
before wage increases:
jack = m + 5
mark = m
after wage increases:
jack = 1.06(m + 5)
mark = 1.06m
difference = 1.06(5)
= 5.30, but you're wasting your time if you calculate 1.06(5) (all you have to notice is that it's a constant; m drops out)
sufficient

(2)
before wage increases:
jack = 4x
mark = 3x
after wage increases:
jack = 1.06(4x) = 4.24x
mark = 1.06(3x) = 3.18x
difference = 1.06x
depends on x
insufficient

answer = a

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could be?

a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100




The important insight for this problem is to realize that the way to minimize the population in the least populous voting district is to have the maximum permitted population in each of the other districts. So you have the least populous district with population, p, and then each of the remaining 10 districts would have a population 10% greater than the least populous district or 1.1p. We know the total city population is 132,000 so:

p+10*(1.1p)=132000
12p=132,000
p=11,000

Of the 800 companies in Company X, 70% have been with the company for at least 10 years. If y of these "long-term"

members were to retire, and no other employee changes were to occur, what value of y would reduce the percent of

"long-term" employees in the company to 60%.

A) 200
B) 160
C) 112
D) 80
E) 56



Assume y=x
The number of people working more than 10 years = 70% of 800 = 560
Hence (560-x)/(800-x)=60%
Thus x=200

OR

The number of long term workers = 70% of 800 = 560
Now if y of the long term workers retired, then long term workers left are 560-y and the number of total employees

= 800-y

Thus (560-y)/(800-y) * 100 = 60
560-y = 480 - 0.6y
80 = 0.4y
y = 200 Ans