GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #232 : Arithmetic

Is $\frac{A}{B}$ a fraction in lowest terms?

Statement 1: is an odd number divisible by 5.

Statement 2: is an even number not divisible by 5.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The two statements together are insufficient. $\frac{35}{12}$ and $\frac{35}{14}$ each satisfy the conditions of both statements, but the first fraction is in lowest terms and the second is not.

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Example Question #3332 : Gmat Quantitative Reasoning

$\frac{M}{N}$ is a fraction in lowest terms. Is its decimal representation a terminating decimal or a repeating decimal?

Statement 1: is a power of 2.

Statement 2: is a multiple of 5.

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The two statements together provide insufficient information.

$\frac{4}{5} = 0.8$ and $\frac{4}{15} = 0.2666...$ are two examples of fractions that satisfy both conditions; note that the first is represented in decimal form by a terminating decimal, and the second, by a repeating decimal.

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Example Question #233 : Arithmetic

Which fraction is larger than $\frac{17}{25}$ ?

Possible Answers:

$\frac{71}{100}$

$\frac{34}{50}$

$\frac{3}{5}$

$\frac{1}{2}$

$\frac{61}{100}$

Correct answer:

$\frac{71}{100}$

Explanation:

From the question, we know that only one of the fractions in the answer choices is larger than $\frac{17}{25}$ . The correct answer must therefore be the largest of the answer choices. This observation is important, because it means we can eliminate some of the answer choices without performing any calculations. For example, $\frac{61}{100}$ is smaller than $\frac{71}{100}$ , so eliminate $\frac{61}{100}$ from the possibilities. $\frac{1}{2}$ is smaller than both $\frac{61}{100}$ and $\frac{71}{100}$ , so eliminate it as well. Similarly, $\frac{34}{50}$ is smaller than $\frac{71}{100}$ , so eliminate $\frac{34}{50}$ too.

This leaves us with only two answer choices: $\frac{3}{5}$ and $\frac{71}{100}$

First consider $\frac{3}{5}$ . We can rewrite this as $\frac{3}{5}=\frac{3\times 5}{5\times 5}=\frac{15}{25}$ , which is clearly smaller than $\frac{17}{25}$ . Eliminate $\frac{3}{5}$ .

By process of elimination, we've thus shown that $\frac{71}{100}$ is the correct answer choice.

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Example Question #6 : Fractions

is a real number. True or false: is an integer.

Statement 1: $\frac{14}{11} N$ is an integer.

Statement 2: $\frac{3}{7} + N$ is an integer.

Possible Answers:

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Explanation:

Statement 1 alone does not prove is or is not an integer.

For example, if N = 11 , then

$\frac{14}{11} N = \frac{14}{11} \cdot 11 = 14$ .

If $N = \frac{11}{14}$ , then

$\frac{14}{11} N = \frac{14}{11} \cdot \frac{11} {14}= 1$ .

is an integer in only one scenario, but Statement 1 is true in both.

Now assume Statement 2 alone, and let $M = \frac{3}{7} + N$ . Then is an integer by Statement 2, and

$M -N= \frac{3}{7}$

Suppose is an integer. Then M -N , the difference of integers, is itself an integer. But we know that this is equal to $\frac{3}{7}$ , which is not an integer, so, by contradiction, is not an integer.

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Example Question #234 : Arithmetic

$\frac{A}{B}$ is a fraction in lowest terms. Is its decimal representation a terminating decimal or a repeating decimal?

Statement 1: is a power of 5.

Statement 2: is a multiple of 7.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of $\frac{A}{B}$ is repeating.

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Example Question #235 : Arithmetic

and are fractions in lowest terms.

True or false: The result a+b can be represented by an integer or a terminating decimal.

Statement 1: Both fractions have powers of 5 in their denominators.

Statement 2: Both fractions have powers of 3 in their numerators.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. Statement 1 says this about both fractions; the sum of terminating decimals is itself an integer or a terminating decimal.

Statement 2 alone provides insuffiicient information. Examine these examples:

$\frac{3}{5} + \frac{9}{5} = \frac{12}{5} = 2.4$

$\frac{3}{7} + \frac{9}{7} = \frac{12}{7} = 1.\overline{714285}$

Both fit the conditions of the main premise and Statement 2, but in only one case is the sum equal to a terminating decimal.

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Example Question #3 : Decimals

and are fractions in lowest terms.

True or false: The result a+b can be represented by an integer or a terminating decimal.

Statement 1: Both denominators are even.

Statement 2: Both denominators are multiples of 3.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:

$\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} = 0.\overline{3}$

$\frac{1}{6} + \frac{5}{6} = \frac{6}{6} = 1$

In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.

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Example Question #241 : Arithmetic

and are fractions in lowest terms.

True or false: The result a b can be represented by an integer or a terminating decimal.

Statement 1: Neither denominator is a multiple of 5.

Statement 2: Both denominators are powers of 2.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. Examine these two examples:

$\frac{1}{3} \times \frac{1}{3} = \frac{1}{9} = 0.\overline{1}$

$\frac{1}{2} \times \frac{1}{4} = \frac{1}{8} = 0.125$

Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.

Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.

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Example Question #242 : Arithmetic

and are fractions in lowest terms.

True or false: The result a b can be represented by an integer or a terminating decimal.

Statement 1: The denominator of is a power of 7.

Statement 2: The denominator of is a power of 3.

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.

$\frac{1}{7} \times \frac{1}{3} = \frac{1}{21} = 0.\overline{037}$

$\frac{3}{7} \times \frac{7}{3} = \frac{21}{21} = 1$

In only one case is the product equivalent to an integer or a terminating decimal.

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Example Question #243 : Arithmetic

and are fractions in lowest terms.

True or false: The result a b can be represented by an integer or a terminating decimal.

Statement 1: The denominator of is three times the numerator of .

Statement 2: The denominator of is six times the numerator of .

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. Rewrite the fractions as follows:

$a = \frac{M}{N}, b= \frac{P}{Q}$ , where GCF(M,N)= GCF (P,Q)= 1 - that is, their lowest-terms representations.

By Statement 1, N = 3P , so $a = \frac{M}{3P}$ . Therefore,

$ab = \frac{M}{3P} \cdot \frac{P}{Q} = \frac{M}{3 } \cdot \frac{1}{Q} = \frac{M}{3Q }$

Since $\frac{M}{3P}$ is in lowest terms, is not a multiple of 3, so the 3 must remain in the denominator, even if the and the can be reduced. Since a fraction which, in lowest terms, has a denominator with any prime factor other than 2 or 5 cannot be represented by an integer or a terminating decimal, Statement 1 proves that has a repeating decimal as its equivalent.

A similar argument can be used to demonstrate that Statement 2 proves the same of .

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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #232 : Arithmetic

Example Question #3332 : Gmat Quantitative Reasoning

Example Question #233 : Arithmetic

Example Question #6 : Fractions

Example Question #234 : Arithmetic

Example Question #235 : Arithmetic

Example Question #3 : Decimals

Example Question #241 : Arithmetic

Example Question #242 : Arithmetic

Example Question #243 : Arithmetic

All GMAT Math Resources

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