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# Is a cubic centimeter of substance S heavier than a cubic centimeter

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
Is a cubic centimeter of substance S heavier than a cubic centimeter  [#permalink]

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06 Feb 2018, 04:42
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Difficulty:

55% (hard)

Question Stats:

56% (01:42) correct 44% (02:11) wrong based on 22 sessions

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Is a cubic centimeter of substance S heavier than a cubic centimeter of substance T ?

(1) A cubic centimeter of S weighs more than 0.25 cubic centimeters of T.

(2) 3 cubic centimeters of T weighs less than 5 cubic centimeters of S.

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Re: Is a cubic centimeter of substance S heavier than a cubic centimeter  [#permalink]

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06 Feb 2018, 22:13
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Bunuel wrote:
Is a cubic centimeter of substance S heavier than a cubic centimeter of substance T ?

(1) A cubic centimeter of S weighs more than 0.25 cubic centimeters of T.

(2) 3 cubic centimeters of T weighs less than 5 cubic centimeters of S.

Let 1 cubic centimeter of S be represented as S only, and 1 cubic centimeter of T be represented as T only. Question asks if S > T (in terms of weight).

(1) S > 0.25*T or S > T/4 or 4S > T.
If S is greater than 1/4 of T, we can't say whether S will be greater than T or not. Eg., if T=4, we are given that S > 1. Now if S = 5 then YES but if S = 2, then NO.
So not sufficient.

(2) 3T < 5S or S > 3T/5 or S > 0.6T.
S is greater than 60% of T, but we cant say whether S will be greater than T or not. Eg., if T=5, we are given that S > 3. Now if S = 6, then YES but if S = 4, then NO.
So not sufficient.

Combining the two statements, we get that:
S > 0.25T and
S > 0.6 T

So basically these two inequations tell us that S > 0.6T. But as explained in second statement, it is not sufficient to get a unique YES or NO answer. So not sufficient.

Re: Is a cubic centimeter of substance S heavier than a cubic centimeter   [#permalink] 06 Feb 2018, 22:13
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