GMAT focus practice exam question and
answers review with solutions 2024
5. The nearest star outside our solar system is approximately 4 x 10^13 kilometers (km) from Earth and
our moon is approximately 380,000 km from Earth. If these distances were scaled down so that the
distance from Earth to our moon was represented by 1 centimeter, then which of the following is closest
to the scaled down distance, in kilometers, from Earth to the nearest star outside our solar system?A.
10B. 100C. 1,000D. 100,000E. 1,000,000 - ANSWER If we denote the scaled down distance from Earth to
Moon by 1 cm', then we have the following unit conversion equation:
1 cm' = 3.8 × 10⁵ km
In addition, we need to consider the following unit conversion equations as well:1 m' = 100 cm'1 km' =
1,000 m'
Now, we simply multiply 4 × 10¹³ km by the corresponding unit conversion factors until all unnecessary
units of measurement cancel out.
(4 × 10¹³ km)(1 cm'/3.8 × 10⁵ km)(1 m'/10² cm')(1 km'/10³ m') == 4/3.8 × 10³ km' ≈ 1 × 10³ km' = 1,000
km'
Answer: C_________________
4. A box contains exactly 7 fuses, 3 of which are defective and 4 of which are not defective. In the bar
graph above, the left and middle bars are the same height and the right bar is half this height. The
heights are intended to represent, respectively, the probabilities of obtaining 0 defective fuses, exactly 1
defective fuse, and 2 defective fuses when 2 fuses are randomly selected without replacement from the
box. However, 1 of the bar heights is incorrect. The correct height is k times the height shown. Which of
the following choices for the bar and the value of k would result in an accurate representation of the
labeled probabilities? A. Middle bar; k = 1/2B. Middle bar; k = 2C. Left bar; k = 1/2D. Left bar; k = 2E.
Right bar; k = 2 - ANSWER 7 fuses (3 def, 4 Ndef) are in the box, from which a random sample of 2 fuses
is selected.Left column:P(0 def) = P(Ndef & Ndef) = 4/7 × 3/6 = 2/7Middle column:P(1 def) = P(def &
Ndef) + P(Ndef & def) = 3/7 × 4/6 + 4/7 × 3/6 = 4/7Right column:P(2 def) = (def & def) = 3/7 × 2/6 =
1/7According to the probabilities above, the ratio of the heights of the columns should be:Left : Middle :
Right = 2 : 4 : 1We see that, in the graph, the heights of the left and right columns are in the correct ratio
of 2 : 1. So, the height of the middle column should be changed.If we double the height of the middle
column by multiplying its height by the factor k = 2, then all three heights will be in the correct
ratio.Answer: B
3. For the rental of a certain type of car, rental agency R charges a fee of $30 per day plus a fee of $0.20
for each mile traveled in excess of 100 miles per day. For the rental of the same type of car, rental agency
S charges a fee of $65 per day with free unlimited mileage. If a car of this type is to be rented for 3 days
and will be driven the same number of miles each day, for what total number of miles will the cost of
renting the car from rental agency R be the same as the cost of renting the car from rental agency S ?A)
352B) 405C) 525D) 750E) 825 - ANSWER Let us work out the rent by each agency by taking y as the
number of miles per day.1) Rental Agency R: 30+0.20(y-100) per day2) Rental Agency S: 65 per day.If
both are equal =
30+0.20(y−100)=65.......15(y−100)=35.......y−100=175.......y=27530+0.20(y−100)=65.......15(y−100)=35......
.y−100=175.......y=275
Since we are looking for miles in 3 days => 3*275 = $825E
, 2. The average (arithmetic mean) of the 5 positive integers, u, w ,x, y, and z is 14, and u < w <x < y < z. If z
is 26, what is the least possible value of the median of the 5 integers?(A) 3(B) 7(C) 8(D) 9(E) 10 - ANSWER
For the unknown integers,u < w < x < y < 26andu + w + x + y + 26 = 14 × 5 = 70The median is the middle
number in the list of 5 items in ascending order, so:median = xIf the sum of some variables is given, then
we can minimize a certain variable by maximizing the others.The maximum value of y is 25. Clearly, w
cannot be greater than "median - 1," and u cannot be greater than "median - 2."Of course, according to
the given conditions, the median must be an integer.Let's now concentrate on the sum of the 5
integers:median - 2 + median - 1 + median + 25 + 26 = 703 × median = 22median = 7.33The median
cannot be less than or equal to 7 because, in this case, the sum of the 5 integers would be less than 70.If
the median, or x, is equal to 8, then w can be equal to 7, and u can be equal to the rest, or 70 - 26 - 25 - 8
- 7 = 4.
Therefore, the least possible value of the median is 8.
Answer: C
6. If S is the sum of all the numbers of the form 1/n, where n is an integer from 33 to 64 inclusive, then S
lies in which of the following intervals?
(A) 0 < S < 1/64(B) 1/64 < S < 1/32(C) 1/32 < S < 1/2(D) 1/2 < S < 1(E) 1 < S < 2 - ANSWER S = 1/33 + 1/34
+ ... + 1/64We see that S is the sum of 64 - 33 + 1 = 32 different fractions. Of these fractions, 1/64 is the
smallest, and 1/33 is the greatest.
Therefore, 32(1/64) < S < 32(1/33)32/64 < S < 32/33 < 33/331/2 < S <1
Answer: D
7. Which of the following is equal to 16(48)716(48)7?A. 8^6B. 8^7C. 6(48)^6D. 8(48)^6E. 8(48)^7 -
ANSWER A) 8^6 vs. (48/6)(48)^6 = 8(48)^6 [The right side is clearly greater.]B) 8^7 = 8(8^6) vs. 8(48)^6
[The right side is clearly greater.]C) 6(48)^6 vs. 8(48)^6 [The right side is clearly greater.]D) 8(48)^6 =
8(48)^6Since we have the correct answer, there's no need to check answer choice E.Answer: D
8. One year ago a window washing service charged $100 for setup and an additional $30 per hour for on-
site washing. This year the company charges $20 for setup and an additional $50 per hour for on-site
washing. Which of the following is equivalent to the percentage change from last year to this year that
the company charges for setup and x hours of on-site washing?A.
100(3x+102x−8)%100(3�+102�−8)%B. 200(x−43x+10)%200(�−43�+10)%C.
200(x−45x+2)%200(�−45�+2)%D. 200(4−x3x+10)%200(4−�3�+10)%E. 200(4−x5x+2)% - ANSWER
percent change = [(new - old)/old] × 100%new amount charged = 20 + 50xold amount charged = 100 +
30xpercent change = [(20 + 50x - 100 - 30x)/(100 + 30x)] × 100% =[(20x - 80)/(30x + 100)] × 100%
=100[(2x - 8)/(3x + 10)]% =200[(x - 4)/(3x + 10)]%
Answer: B
9. At a recent sale, Harue bought various numbers of 5 types of school supplies - markers, pens, pencils,
erasers, and notebooks - each advertised with a different pricing strategy. Harue bought 4 markers for
the price of 3, 3 pens for the price of 2, 5 pencils for the price of 3, 2 erasers for the price of 1, and 5
notebooks for the price of 2. One of the 5 types of school supplies was advertised as "Buy one, get one
at 50% off." Which type?A. MarkersB. PensC. PencilsD. ErasersE. Notebooks - ANSWER If x is the regular
price of an item, then "Buy one, get one at 50% off" means "Pay a total of x + 0.5x = 1.5x if you buy two
answers review with solutions 2024
5. The nearest star outside our solar system is approximately 4 x 10^13 kilometers (km) from Earth and
our moon is approximately 380,000 km from Earth. If these distances were scaled down so that the
distance from Earth to our moon was represented by 1 centimeter, then which of the following is closest
to the scaled down distance, in kilometers, from Earth to the nearest star outside our solar system?A.
10B. 100C. 1,000D. 100,000E. 1,000,000 - ANSWER If we denote the scaled down distance from Earth to
Moon by 1 cm', then we have the following unit conversion equation:
1 cm' = 3.8 × 10⁵ km
In addition, we need to consider the following unit conversion equations as well:1 m' = 100 cm'1 km' =
1,000 m'
Now, we simply multiply 4 × 10¹³ km by the corresponding unit conversion factors until all unnecessary
units of measurement cancel out.
(4 × 10¹³ km)(1 cm'/3.8 × 10⁵ km)(1 m'/10² cm')(1 km'/10³ m') == 4/3.8 × 10³ km' ≈ 1 × 10³ km' = 1,000
km'
Answer: C_________________
4. A box contains exactly 7 fuses, 3 of which are defective and 4 of which are not defective. In the bar
graph above, the left and middle bars are the same height and the right bar is half this height. The
heights are intended to represent, respectively, the probabilities of obtaining 0 defective fuses, exactly 1
defective fuse, and 2 defective fuses when 2 fuses are randomly selected without replacement from the
box. However, 1 of the bar heights is incorrect. The correct height is k times the height shown. Which of
the following choices for the bar and the value of k would result in an accurate representation of the
labeled probabilities? A. Middle bar; k = 1/2B. Middle bar; k = 2C. Left bar; k = 1/2D. Left bar; k = 2E.
Right bar; k = 2 - ANSWER 7 fuses (3 def, 4 Ndef) are in the box, from which a random sample of 2 fuses
is selected.Left column:P(0 def) = P(Ndef & Ndef) = 4/7 × 3/6 = 2/7Middle column:P(1 def) = P(def &
Ndef) + P(Ndef & def) = 3/7 × 4/6 + 4/7 × 3/6 = 4/7Right column:P(2 def) = (def & def) = 3/7 × 2/6 =
1/7According to the probabilities above, the ratio of the heights of the columns should be:Left : Middle :
Right = 2 : 4 : 1We see that, in the graph, the heights of the left and right columns are in the correct ratio
of 2 : 1. So, the height of the middle column should be changed.If we double the height of the middle
column by multiplying its height by the factor k = 2, then all three heights will be in the correct
ratio.Answer: B
3. For the rental of a certain type of car, rental agency R charges a fee of $30 per day plus a fee of $0.20
for each mile traveled in excess of 100 miles per day. For the rental of the same type of car, rental agency
S charges a fee of $65 per day with free unlimited mileage. If a car of this type is to be rented for 3 days
and will be driven the same number of miles each day, for what total number of miles will the cost of
renting the car from rental agency R be the same as the cost of renting the car from rental agency S ?A)
352B) 405C) 525D) 750E) 825 - ANSWER Let us work out the rent by each agency by taking y as the
number of miles per day.1) Rental Agency R: 30+0.20(y-100) per day2) Rental Agency S: 65 per day.If
both are equal =
30+0.20(y−100)=65.......15(y−100)=35.......y−100=175.......y=27530+0.20(y−100)=65.......15(y−100)=35......
.y−100=175.......y=275
Since we are looking for miles in 3 days => 3*275 = $825E
, 2. The average (arithmetic mean) of the 5 positive integers, u, w ,x, y, and z is 14, and u < w <x < y < z. If z
is 26, what is the least possible value of the median of the 5 integers?(A) 3(B) 7(C) 8(D) 9(E) 10 - ANSWER
For the unknown integers,u < w < x < y < 26andu + w + x + y + 26 = 14 × 5 = 70The median is the middle
number in the list of 5 items in ascending order, so:median = xIf the sum of some variables is given, then
we can minimize a certain variable by maximizing the others.The maximum value of y is 25. Clearly, w
cannot be greater than "median - 1," and u cannot be greater than "median - 2."Of course, according to
the given conditions, the median must be an integer.Let's now concentrate on the sum of the 5
integers:median - 2 + median - 1 + median + 25 + 26 = 703 × median = 22median = 7.33The median
cannot be less than or equal to 7 because, in this case, the sum of the 5 integers would be less than 70.If
the median, or x, is equal to 8, then w can be equal to 7, and u can be equal to the rest, or 70 - 26 - 25 - 8
- 7 = 4.
Therefore, the least possible value of the median is 8.
Answer: C
6. If S is the sum of all the numbers of the form 1/n, where n is an integer from 33 to 64 inclusive, then S
lies in which of the following intervals?
(A) 0 < S < 1/64(B) 1/64 < S < 1/32(C) 1/32 < S < 1/2(D) 1/2 < S < 1(E) 1 < S < 2 - ANSWER S = 1/33 + 1/34
+ ... + 1/64We see that S is the sum of 64 - 33 + 1 = 32 different fractions. Of these fractions, 1/64 is the
smallest, and 1/33 is the greatest.
Therefore, 32(1/64) < S < 32(1/33)32/64 < S < 32/33 < 33/331/2 < S <1
Answer: D
7. Which of the following is equal to 16(48)716(48)7?A. 8^6B. 8^7C. 6(48)^6D. 8(48)^6E. 8(48)^7 -
ANSWER A) 8^6 vs. (48/6)(48)^6 = 8(48)^6 [The right side is clearly greater.]B) 8^7 = 8(8^6) vs. 8(48)^6
[The right side is clearly greater.]C) 6(48)^6 vs. 8(48)^6 [The right side is clearly greater.]D) 8(48)^6 =
8(48)^6Since we have the correct answer, there's no need to check answer choice E.Answer: D
8. One year ago a window washing service charged $100 for setup and an additional $30 per hour for on-
site washing. This year the company charges $20 for setup and an additional $50 per hour for on-site
washing. Which of the following is equivalent to the percentage change from last year to this year that
the company charges for setup and x hours of on-site washing?A.
100(3x+102x−8)%100(3�+102�−8)%B. 200(x−43x+10)%200(�−43�+10)%C.
200(x−45x+2)%200(�−45�+2)%D. 200(4−x3x+10)%200(4−�3�+10)%E. 200(4−x5x+2)% - ANSWER
percent change = [(new - old)/old] × 100%new amount charged = 20 + 50xold amount charged = 100 +
30xpercent change = [(20 + 50x - 100 - 30x)/(100 + 30x)] × 100% =[(20x - 80)/(30x + 100)] × 100%
=100[(2x - 8)/(3x + 10)]% =200[(x - 4)/(3x + 10)]%
Answer: B
9. At a recent sale, Harue bought various numbers of 5 types of school supplies - markers, pens, pencils,
erasers, and notebooks - each advertised with a different pricing strategy. Harue bought 4 markers for
the price of 3, 3 pens for the price of 2, 5 pencils for the price of 3, 2 erasers for the price of 1, and 5
notebooks for the price of 2. One of the 5 types of school supplies was advertised as "Buy one, get one
at 50% off." Which type?A. MarkersB. PensC. PencilsD. ErasersE. Notebooks - ANSWER If x is the regular
price of an item, then "Buy one, get one at 50% off" means "Pay a total of x + 0.5x = 1.5x if you buy two
