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GMAT Question Patterns in Arithmetic
We have gone through the OG 13 and analyzed all of the questions to spot the most common patterns. This discussion is dedicated to the types of arithmetic problems that could appear on the test. If you have spotted any other patterns, please let me know.
Background:
GMAT arithmetic problems deal with operations on fractions, decimals and irrational numbers. Most of them are quit straightforward and generally are encountered in problem solving section.
Typical questions:
We have gone through the OG 13 and analyzed all of the questions to spot the most common patterns. This discussion is dedicated to the types of arithmetic problems that could appear on the test. If you have spotted any other patterns, please let me know.
Background:
GMAT arithmetic problems deal with operations on fractions, decimals and irrational numbers. Most of them are quit straightforward and generally are encountered in problem solving section.
Typical questions:
Arithmetic: Fractions and Decimals
\(\frac{1}{1+\frac{1}{3}}-\frac{1}{1+\frac{1}{2}}\)
(A) -1/3
(B) -1/6
(C) -1/12
(D) 1/12
(E) 1/3
Discussed HERE
\(1-(\frac{1}{2}-\frac{2}{3})=\)
(A) 6/5
(B) 7/6
(C) 6/7
(D) 5/6
(E) 0
Discussed HERE
1/2 + [(2/3 * 3/8)/4] - 9/16 =
(A) 29/16
(B) 19/16
(C) 15/16
(D) 9/13
(E) 0
Discussed HERE
\(\frac{1}{0.75-1}=\)
(A) -4
(B) -0.25
(C) 0.25
(D) 0.75
(E) 4
Discussed HERE
\(\frac{1}{1+\frac{1}{3}}-\frac{1}{1+\frac{1}{2}}\)
(A) -1/3
(B) -1/6
(C) -1/12
(D) 1/12
(E) 1/3
Discussed HERE
\(1-(\frac{1}{2}-\frac{2}{3})=\)
(A) 6/5
(B) 7/6
(C) 6/7
(D) 5/6
(E) 0
Discussed HERE
1/2 + [(2/3 * 3/8)/4] - 9/16 =
(A) 29/16
(B) 19/16
(C) 15/16
(D) 9/13
(E) 0
Discussed HERE
\(\frac{1}{0.75-1}=\)
(A) -4
(B) -0.25
(C) 0.25
(D) 0.75
(E) 4
Discussed HERE
Arithmetic: Inequalities
The sum \(\frac{7}{8}+\frac{1}{9}\) is between
(A) \(\frac{1}{2}\) and \(\frac{3}{4}\)
(B) \(\frac{3}{4}\) and 1
(C) 1 and \(1\frac{1}{4}\)
(D) \(1\frac{1}{4}\) and \(1\frac{1}{2}\)
(E) \(1\frac{1}{2}\) and 2
Discussed HERE
The sum \(\frac{7}{8}+\frac{1}{9}\) is between
(A) \(\frac{1}{2}\) and \(\frac{3}{4}\)
(B) \(\frac{3}{4}\) and 1
(C) 1 and \(1\frac{1}{4}\)
(D) \(1\frac{1}{4}\) and \(1\frac{1}{2}\)
(E) \(1\frac{1}{2}\) and 2
Discussed HERE
Arithmetic: Exponents
0.1+0.1^2+0.1^3=
(A) 0.1
(B) 0.111
(C) 0.1221
(D) 0.2341
(E) 0.3
Discussed HERE
(0.0036)(2.8) / (0.04)(0.1)(0.003) =
(A) 840.0
(B) 84.0
(C) 8.4
(D) 0.84
(E) 0.084
Discussed HERE
\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\)
(A) 10^(-8)
(B) 3*10^(-8)
(C) 3*10^(-4)
(D) 2*10^(-4)
(E) 10^(-4)
Discussed HERE
\((\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1}=\)
(A) (1/2)^(-48)
(B) (1/2)^(-11)
(C) (1/2)^(-6)
(D) (1/8)^(-11)
(E) (1/8)^(-6)
Discussed HERE
The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is how many times the value of 2^(-17)?
A. 3/2
B. 5/2
C. 3
D. 4
E. 5
Discussed HERE
0.1+0.1^2+0.1^3=
(A) 0.1
(B) 0.111
(C) 0.1221
(D) 0.2341
(E) 0.3
Discussed HERE
(0.0036)(2.8) / (0.04)(0.1)(0.003) =
(A) 840.0
(B) 84.0
(C) 8.4
(D) 0.84
(E) 0.084
Discussed HERE
\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\)
(A) 10^(-8)
(B) 3*10^(-8)
(C) 3*10^(-4)
(D) 2*10^(-4)
(E) 10^(-4)
Discussed HERE
\((\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1}=\)
(A) (1/2)^(-48)
(B) (1/2)^(-11)
(C) (1/2)^(-6)
(D) (1/8)^(-11)
(E) (1/8)^(-6)
Discussed HERE
The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is how many times the value of 2^(-17)?
A. 3/2
B. 5/2
C. 3
D. 4
E. 5
Discussed HERE
Arithmetic: Roots
\(\sqrt{16*20+8*32}=\)
(A) \(4\sqrt{20}\)
(B) 24
(C) 25
(D) \(4\sqrt{20}+8\sqrt{2}\)
(E) 32
Discussed HERE
\(\sqrt{80}+\sqrt{125} =\)
(A) \(9\sqrt{5}\)
(B) \(20\sqrt{5}\)
(C) \(41\sqrt{5}\)
(D) \(\sqrt{205}\)
(E) 100
Discussed HERE
\(\sqrt{16*20+8*32}=\)
(A) \(4\sqrt{20}\)
(B) 24
(C) 25
(D) \(4\sqrt{20}+8\sqrt{2}\)
(E) 32
Discussed HERE
\(\sqrt{80}+\sqrt{125} =\)
(A) \(9\sqrt{5}\)
(B) \(20\sqrt{5}\)
(C) \(41\sqrt{5}\)
(D) \(\sqrt{205}\)
(E) 100
Discussed HERE
Arithmetic: Approximation
Many GMAT arithmetic problems require approximations, for example:
The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
(A) 7.1 x 10^8
(B) 5.9 x 10^9
(C) 1.6 x 10^10
(D) 1.6 x 10^11
(E) 5.9 x 10^11
Discussed HERE
M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?
(A) 1/3 < M < 1/2
(B) 1/5 < M < 1/3
(C) 1/7 < M < 1/5
(D) 1/9 < M < 1/7
(E) 1/12 < M < 1/9
Discussed HERE
If \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\), then the value of M is:
A. Less than 3
B. Equal to 3
C. Between 3 and 4
D. Equal to 4
E. Greater than 4
Discussed HERE
The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Discussed HERE
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to
A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5
Discussed HERE
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?
A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4
Discussed HERE
Many GMAT arithmetic problems require approximations, for example:
The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
(A) 7.1 x 10^8
(B) 5.9 x 10^9
(C) 1.6 x 10^10
(D) 1.6 x 10^11
(E) 5.9 x 10^11
Discussed HERE
M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?
(A) 1/3 < M < 1/2
(B) 1/5 < M < 1/3
(C) 1/7 < M < 1/5
(D) 1/9 < M < 1/7
(E) 1/12 < M < 1/9
Discussed HERE
If \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\), then the value of M is:
A. Less than 3
B. Equal to 3
C. Between 3 and 4
D. Equal to 4
E. Greater than 4
Discussed HERE
The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Discussed HERE
If S is the sum of reciprocals of a list of consecutive integers from 45 to 54, inclusive, S is approximately equal to
A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5
Discussed HERE
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?
A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4
Discussed HERE
Arithmetic: Conversions
Some arithmetic questions deal with conversions, such as to convert miles into meters, miles per hour into meters per second, liters into cubic meters, etc. Note that you don't need to know how many meters are in 1 mile, or how many cubic meters are in 1 liter, such kind of info will be provided in the question.
If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 2 miles?
(A) 10/3
(B) 3
(C) 6/5
(D) 1/3
(E) 3/10
Discussed HERE
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5
Discussed HERE
The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5280 feet = 1 mile)
A. \((\frac{20}{5280})(\frac{60^2}{0.5})\)
B. \((\frac{20}{5280})(\frac{60}{0.5})\)
C. \((\frac{20}{5280})(\frac{0.5}{60^2})\)
D. \(\frac{(20)(5280)}{(60^2)(0.5)}\)
E. \(\frac{(20)(5280)}{(60)(0.5)}\)
Discussed HERE
A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
A. 92
B. 90
C. 82
D. 78
E. 75
Discussed HERE
Some arithmetic questions deal with conversions, such as to convert miles into meters, miles per hour into meters per second, liters into cubic meters, etc. Note that you don't need to know how many meters are in 1 mile, or how many cubic meters are in 1 liter, such kind of info will be provided in the question.
If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 2 miles?
(A) 10/3
(B) 3
(C) 6/5
(D) 1/3
(E) 3/10
Discussed HERE
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5
Discussed HERE
The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5280 feet = 1 mile)
A. \((\frac{20}{5280})(\frac{60^2}{0.5})\)
B. \((\frac{20}{5280})(\frac{60}{0.5})\)
C. \((\frac{20}{5280})(\frac{0.5}{60^2})\)
D. \(\frac{(20)(5280)}{(60^2)(0.5)}\)
E. \(\frac{(20)(5280)}{(60)(0.5)}\)
Discussed HERE
A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
A. 92
B. 90
C. 82
D. 78
E. 75
Discussed HERE
Theory on arthemtic is HERE.
All OG13 questions with solutions are HERE.
PS questions on arithmetic are HERE.
DS questions on arithmetic are HERE.
All OG13 questions with solutions are HERE.
PS questions on arithmetic are HERE.
DS questions on arithmetic are HERE.
15 Apr 2025, 03:46
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