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# GMAT Question Patterns: Arithmetic

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Math Expert
Joined: 02 Sep 2009
Posts: 58418

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28 Jan 2013, 06:35
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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:

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

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

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

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

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

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

Theory on arthemtic is HERE.
All OG13 questions with solutions are HERE.
PS questions on arithmetic are HERE.
DS questions on arithmetic are HERE.

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Re: GMAT Question Patterns: Arithmetic  [#permalink]

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28 Jan 2013, 12:08
6
Here we are
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##### General Discussion
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Joined: 02 Sep 2009
Posts: 58418
Re: GMAT question patterns: Arithmetic  [#permalink]

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28 Jan 2013, 06:38
2
1
Please suggest arithmetic questions which are typical for the GMAT.

P.S. We'll be covering one topic per week.
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Re: GMAT Question Patterns: Arithmetic  [#permalink]

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02 Feb 2013, 09:59
The link to the following problem seem to be broken:

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

I would surely appreciate to learn a quick and efficient way to approximate this.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 58418
Re: GMAT Question Patterns: Arithmetic  [#permalink]

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02 Feb 2013, 10:38
1
georgesk wrote:
The link to the following problem seem to be broken:

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

I would surely appreciate to learn a quick and efficient way to approximate this.

Thanks

Here it is: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html

Hop it helps.

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Re: GMAT Question Patterns: Arithmetic  [#permalink]

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20 Mar 2013, 10:08
where can I find the other topics under this similar tag. What other topics have been covered under GMAT question Patterns?
Math Expert
Joined: 02 Sep 2009
Posts: 58418
Re: GMAT Question Patterns: Arithmetic  [#permalink]

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20 Mar 2013, 10:16
fozzzy wrote:
where can I find the other topics under this similar tag. What other topics have been covered under GMAT question Patterns?

We have one more topic on remainders: remainders-144665.html
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Re: GMAT Question Patterns: Arithmetic  [#permalink]

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27 Aug 2015, 23:42
4
Thanks Bunuel! Great resource.
Could be please consolidate patterns from other topics as well. Especially Percentages, Ratio Prop. etc? It would really help!
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Re: GMAT Question Patterns: Arithmetic  [#permalink]

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29 Sep 2018, 12:51
$$\frac{1}{1+\frac{1}{3}}-\frac{1}{1+\frac{1}{2}}$$
How do I interpret these brackets?

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Re: GMAT Question Patterns: Arithmetic  [#permalink]

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29 Sep 2018, 13:00
kalyani9503 wrote:
$$\frac{1}{1+\frac{1}{3}}-\frac{1}{1+\frac{1}{2}}$$
How do I interpret these brackets?

Sent from my Mi A1 using GMAT Club Forum mobile app

kalyani9503,

What brackets? The expression can be evaluated by evaluating the denominators first .. so 1+1/3 is 4/3 and 1+1/2 is 3/2.
Now the expression is 3/4 - 2/3 = (9-8)/12= 1/12.

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Re: GMAT Question Patterns: Arithmetic  [#permalink]

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27 Mar 2019, 23:01
Thank you Bunuel! Excellent post
Re: GMAT Question Patterns: Arithmetic   [#permalink] 27 Mar 2019, 23:01
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