# Percentage on the SAT

## How do we calculate SAT problems involving percent?

Question Number 1
SAT PROBLEM
4th problem in a 25 problem section

A certain state requires that an applicant for a driver's license answer at least 80 percent of the questions on a written test correctly. If the test has 30 questions on it, at least how many of these questions must be answered correctly?

• 20
• 21
• 22
• 23
• 24
( Saturday/11.1996 #4) p. 370
 E) 80% = . 80 .80 *30=24 METHOD: Since this is just straightforward arithmetic here. I'll forgive you if you just did the steps up above without any fancy test prep techniques like SUBSTITUTING IN etc...

Question Number 2
SAT PROBLEM
#7 in a 25 problem section

What percent of 50 is 6?

• 3 %
• 8.33%
• 12%
• 30%
• 88.33%
( Saturday/1.200) p.524
 C) 12 % METHOD: Make sure you ballpark estimate this one at some point before committing to your answer.

Question Number 3
SAT PROBLEM
#7 in a 25 problem section

If r is 35 percent of p and s is 45 percent of p, what is r + s in terms of p?

• 0.4p
• 0.5p
• 0.6p
• 0.7p
• 0.8p
( Saturday/1.2000 #7) p.524 *
 E) .45p + .35p= 0.8p

Question Number 4
SAT PROBLEM
9th problem in a 25 problem section

What percent of 50 is 6?

(Sunday/5.1997 #4) p. 484
 C) 12% 6/50=12/100 METHOD: ESTIMATING should serve you well here. You should be able to estimate that the answer is going to be about twice of 6.   This is just converting from a fraction with denominator 50 to a fraction with denominator 100(which is what a percent is).

 Question Number 5 SAT PROBLEM #11 in a 25 problem section 75 percent of 88 is the same as 60 percent of what number? 100 103 105 108 110 ( Saturday/1.1997 #11) p. 405 * E) .75*88=66 .60 *110=66 TEST METHOD: WORK IN REVERSE from Answers Hopefully, you didn't waste time trying to figure out how to solve this algebriacally. (Impress your Math teacher in class with your algebraic magic; save time on a standardized tests like the SAT with whatever method will most quickly get you the answer.) The most time-efficient way to solve this is .75*88=66 Multiply .6 ( or 60% ) by each answer choice until you get 66. The correct answer, E, is the one that works.

 Question Number 6 SAT PROBLEM #17 in a 25 problem section A store has 660 bocks in stock. If 30 percent of these books are on sale, how many books are not on sale? (Student Generated Response) ( Saturday/5.2002 #17) p. 665 * 462 KEYWORD:  NOT--they even underlined it for you!!!! TRAP: If you got this wrong, you either A) fell into the common trap of ignoring the all important stndardized test word "not" and therefore you probably found the number of books that are on sale. B) Probably just made some silly arithmetic error.

Question Number 7

SAT PROBLEM

A total of 60 advertisements were sold for a school yearbook. If 20 percent of the first 20 sold were in color, 40 percent of the next 30 sold were in color, and 80 percent of the last 10 sold were in color, what percent of the 60 advertisements were in color?

 C. 40%

Question Number 8

SAT PROBLEM
(#13 of 25)

If x > 0, what is 30 percent of 15x?

• 0.5x
• 2x
• 4.5x
• 5x
• 45x
• ( Saturday/11.1996 #13) p.372 *
 C) .3(15x)=4.5x

Question Number 9

HARD SAT PROBLEM:

A dress is selling for \$100 after a 20 percent discount. What was the original selling price?

• \$ 200
• \$125
• \$120
• \$80
• \$75
( taken from Princeton Review's Cracking the New SAT ) #17
 B .2 (125)=100 METHOD: Use the multiple choice answers and WORK IN REVERSE. Which answer times .2 is 100? This is a difficult question, a number 17, so you should be very suspicious of C and D, both of which are just too clean and easy.

Question Number 10

MEDIUM-HARD SAT PROBLEM
The percent increase from 8 to 14 is equal to the percent increase from 20 to what?

• 14
• 26
• 28
• 32
• 35
(#7 out of 10 Satuday/1.2002 SAT) p.637
 E) 35 METHOD: Work in Reverse!

Question Number 11

SAT PROBLEM
( 7th out 10 problems)

Pat has s grams of strawberries and uses 40 percent of the strawberries to make pies, each of which requires p grams. The rest of the strawberries are used to make pints of jam, each of which requires j grams. Which of the following gives the number of pints of jam Pat can make?
• (2s)/5p
• (2s)/5j
• (3s)/5j
• (3p)/5s
• (3sj)/5
(Sunday/5.1997 SAT) #7 p. 508 *
 C) (3s)/5j Another tough SAT question. A few helpful hints. First--forget about p, it's a meaningless variable meant to throw you off. Second--40 percent is gone so .6s is left which is the same as 3s/5. I'll leave it to you to try to figure out how j works.

Question Number 12
HARD SAT PROBLEM
(22nd out of 25 problems)

A person slices a pie into k equal pieces and eats on piece. In terms of k, what percent of the pie is left?

 B

 Question Number 13 HARD SAT PROBLEM ( 21st out  of 25s) S is the sum of the first 100 consecutive positive even integers, and T is the sum of the first 100 consecutive positive integers. S is what percent greater than T ? 100% 50% 10% 2% 1% (Sunday/5.2002 SAT) #21 p. 575 A. Eliminate some obvious wrong ones E. 1% , D. 2%, C. 10% Remember to always estimate and have a rough idea of the answers. Even if you can't answer this one you should be able to elimate those the three above and have 50-50 odds of getting the right answer on a very challenging SAT question. Tip for solving this--realize that you can conveniently add up either set by taking the smallest and largest then working inwards. For example, consider the consecutive positive even integers the smallest number 0 and the largest 100 add up to 100; work inwards --1 and 99 also add up to 100. This tip should help you begin on the problem. Another thing I'll leave for you to puzzle out--what happens at the number 50?

 Question Number 14 HARD SAT PROBLEM ( 25 th problem out of 25 problems ) A store charges \$28 for a certain type of sweater. This price is 40 percent more than the amount it costs the store to buy one of these sweaters. At an end-of-season sale, store employees can purchase any remaining sweaters at 30 percent off the store's cost. How much would it cost an employee to purchase a sweater of this type at this sale? \$ 8.40 \$14.00 \$19.60 \$ 20.00 \$ 25.20 (Saturday/5.1997 SAT #10) p. 472 B. A question only for mavens of percentage problems or standardized test-taking sadomasichists. First off, recognize that \$28=1.4 times the cost to the store; ((\$28)/1.4)=20Employees get 30% off this amount 20-(.3*20)=14 Note: ETS gives this a 5 difficulty rating, the rating for the toughest questions.