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University of Cambridge ESOL Examinations

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During a sale Arianna purchases a sweater Listed at $100. Win 20% off and 7% sale tax, how much did she pay for the discounted sweater?

Correct answer

C. 20% of $100 is just $20. So the sale price is $100 - $20 = $80.
7% tax on $80 is (.07)$80 = $5.60. The total price is then $80 + $5.60 = $85.60.

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Franco decides to purchase a new washing machine that sells for $1,100. After making a down payment of $125, he willpay of the remainder in monthly payments of $75. How many months will it tale for Franco to pay of the new washing machine?

Correct answer

D. $1,100 - $125 = $975. At $74 per month, it will take $975 / $75 = 13 month.

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An electronics store owner purchases DVDs from his supplier, paying $270.80 for 20 DVDs. He then sells them to his customers during a special sale, charging $53.01 for 3 DVDs. How much profit, per DVD, does the owner make during the special sale?

Correct answer

A. The store owner pays $270.80 ÷ 20 = $13.54 per DVD. He sells them for $53.01 ÷ 3 = $17.67. His profit per DVD is therefore $17.67 — $13.54 = $4.13.

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If 10 boys averaged 78% on a test for which 15 girls averaged 89%, what is the test average for all 25 students?

Correct answer

C. The class average can be found as follows: 84.6%

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In a set of 15 different integers, which of the following changes would NOT effect the value of the median of these 15 integers?

Correct answer

B. Since the median is the middle of the list of the set of integers, adding 11 to the largest integer will not affect the median. The other option—which is not one the given choices—would be to subtract some positive integer from the smallest number in the set.

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The shoes sizes of 10 men are 8, 10, 9, 12, 7, 10, 10, 11, 6, and 7. How much greater than the mode is the median?

Correct answer

B. Listing the shoe sizes from small to large, you have: 6, 7, 7, 8, 9, 10, 10, 10, 11, 12 The mode (most frequent shoe size) is 10. The median (the middle of the list) would be the average of 9 and 10, which gives 9.5. Notice that since you have an even number (10) of shoe sizes, you had to find the average of the fifth and sixth shoe sizes (9 and 10) to compute the median.

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How many two-digit positive integers are multiples of both 2 and 5?

Correct answer

B. If the positive integer is a multiple of both 3 and 5, it must also be a multiple of 15. So our two-digit multiples of 15 are: 15, 30, 45, 60, 75, and 90. So our correct answer is 6 two-digit multiples of 15.

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The first four numbers in a patterned sequence of positive integers are 1, 2, 4, 8,... . What is the tenth integer in this sequence?

Correct answer

C. The integers double as you move from one term of the sequence to the next. Therefore, the first ten integers in the sequence are: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512.

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Yuri deposits $100 into a new savings account that pays him 3% interest compounded annually. What is the accumulated value of this deposit 6 years after the day of the initial deposit?

Correct answer

B. Since the annual interest rate is 3%, the value of the account one year is 1.03 times the previous year’s value. After 6 years, the account will be worth $100 x (1.03)6 = $119.41.

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A culture of 207 bacteria triples every 12 minutes. What will the bacterial count 2 hours after the original culture of 207 was established?

Correct answer

C. A 2-hour time period represents 120 minutes. This is 10 of the 12-minute time periods in which the bacteria triples. So after 120 minutes, the initial count of 207 will grow to 207×310.

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If x and y are positive integers, and are not both even, which of the following must be even?

Correct answer

E. By default, Choice E must therefore be correct. Just to double-check, you have: 4(x + y) — 2 = 4(any number) — even = even — even = even

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Ling rides his bicycle a distance of 40 miles in 5 hours and then returns the same distance in only 4 hours. What is his average rate, in miles/hour, for the entire trip?

Correct answer

B. Average rate =To compute the time going and returning, you need to use time = dist/time.

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In a one-week period, the price of regular unleaded gasoline went from $2.50/gallon to $2.75/gallon. What was the percent increase in the price of a gallon of regular unleaded gasoline?

Correct answer

B. $2.75 - $2.50 = $0.25. Then $0.25/$2.50=1/10= 10% increase in price of gasoline

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Serena has $500 in a savings account that pays 4% simple interest per year. If she does not deposit or withdraw from this savings account, how much money will be in Serena’s savings account after 3 years?

Correct answer

C. Simple interest = principal x rate x time

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Number Line: Order, Consecutive Numbers, Fractions, Betweenness

In the diagram above, points A, B, C, D, E, and F are equally spaced on the number line. If M is the midpoint of AB and N is the midpoint of DE, what is the distance from M to N?

Correct answer

A. In the figure above, points B, C, D, and E have been labeled with their respective coordinates: 3.2, 3.4, 3.6, and 3.8. Since M is the midpoint of AB, the coordinate of point M is 3.1. Since N is the midpoint of DE, the coordinate of point E is 3.7. Therefore the distance from M to N is 3.7 −3.1= 0.6

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On a number line, points A, B, C, D, and E have respective coordinates a, b, c, d, and e but not necessarily in that order. If c <d, point A is between points C and D, point D is between points A and E, which of the following is a possible order of the points A, B, C, D, and E?

Correct answer

D. Point B, with coordinate b, can be located anywhere. Choice D is the only choice given a possible order.

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v, w, x, y, and z are consecutive odd integers, not necessarily in that order. If x — 4 = z, y + 6 = x, and w > v, which of the following is the correct order for the integers v, w, x, y, and z?

Correct answer

From the first piece of data, x — 4 = z, you get x = z + 4; so z is less than x, and there is one other odd integer between z and x, as shown below: z, __, xFrom the second piece of data, y + 6= x, you know there are two other odd integers between x and y combined with the figure above, you have the series below:y, z,__, x, __ Then since w > v, the final order is as follows: y, z, v, x, w, corresponding with Choice A.

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If S is the set of perfect squares less than 100, and C is the set of perfect cubes less than 100, what is S ∩ C?

Correct answer

D. S = {1, 4, 9, 16, 25, 36, 49, 64, 81} and C = {1, 8, 27, 64}. S ∩ C is the «intersection» of the two sets. The integers common to both sets are only 1 and 64. So the correct answer is the set {1, 64}.

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If A is the set of positive odd integers less than 21, and T is the set of positive multiples of 3 less than 21, what is A ∪ T?

Correct answer

C. A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} and T = {3, 6, 9, 12, 15, 18}. A ? T is the «union» of the two sets. The integers belonging to either one of the sets are {1, 3, 5, 6, 7, 9, 11, 13, 15, 17, 18, 19}.

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M is the set of integers that can be written as √n- 3, where n is a nonzero integer. Which of the following integers is a member of set M?
I. 4
II. 5
III. 7

Correct answer

E. Checking the answer choices one at a time, you have:
I. 4: 4 can be written as — 3 = 7 — 3 = 4
II. 5: 5 can be written as — 3 = 8 — 3 = 5
III. 7: 7 can be written as — 3 = 10 — 3 = 7

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At a party, the ratio of males to females is 3 : 4. Which of the following could NOT be the total number of people at the party?

Correct answer

C. Since the ration of males to females is 3 parts to 4 parts, the number of people at the party must be a multiple of 7 parts. Choice C, 44, is not a multiple of 7.

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If r/m = 2/3 and m/c = 4/5, what is the value of r/c?

Correct answer

C. Notice that r/m x m/c = r/c, which is the ratio you are trying to find. Substituting the numerical values for the ratios on the left in the equation above, you have 2/3 x 4/5 = 8/15

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A special snack mix uses raisins, peanuts, and chocolate candies in the ratio 1 : 2 : 5, respectively. In a snack mix of 112 ounces, how many ounces of chocolate candies are used?

Correct answer

E. If you write your raisins to peanuts to candies ration as 1x : 2x : 5x, you will have
1x + 2x + 5x = 112
                8x = 112
               so x = 14.
Therefore the number of ounces of candies will be 5x = 5(14) = 70.

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