If A and B are consecutive positive integers less than 100 : GMAT Data Sufficiency (DS)
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# If A and B are consecutive positive integers less than 100

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If A and B are consecutive positive integers less than 100 [#permalink]

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05 Apr 2013, 21:23
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If A and B are consecutive positive integers less than 100, what is the value of B?

(1) A is the cube of an integer.
(2) B is the square of an integer.
[Reveal] Spoiler: OA
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Re: If A and B are consecutive positive integers less than 100 [#permalink]

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05 Apr 2013, 22:13
Nichols wrote:
If A and B are consecutive positive integers less than 100, what is the value of B?

1. A is the cube of an integer.
2. B is the square of an integer.

1.) Insufficient, doesn't tell us anything about B.

This statement implies cube root of A<5. $$5^3=125$$, $$4^3=64$$.

2.) Insufficient, this statement tells us $$\sqrt{B}<10$$.

1&2.) Sufficient. Taken together cube root of A<5 and $$\sqrt{B}<10$$ AND consecutive integers, the only values that meet the given conditions are $$A=2^3=8$$ and $$B=3^2=9$$
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Re: If A and B are consecutive positive integers less than 100 [#permalink]

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05 Apr 2013, 22:21
1. A can be 1, 8, 27, or 64. B can be 1, 7, 9, 26, 28, 63, or 65. Not Sufficient.
2. B can be 1, 4, 9, 16, 25, 36, 49, 64, or 81. Not sufficient.

Together: Only 8 and 9 are consecutive cube and square numbers. So B is 9. Sufficient.

Re: If A and B are consecutive positive integers less than 100   [#permalink] 05 Apr 2013, 22:21
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# If A and B are consecutive positive integers less than 100

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