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If the sum of the three different numbers is 54, what is the

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by fskilnik@GMATH » Fri Nov 02, 2018 3:06 pm

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BTGmoderatorLU wrote:Source: GMAT Prep

If the sum of the three different numbers is 54, what is the largest number?

1) The largest number is twice the smallest number.
2) The sum of the two smaller numbers is 30.
$$\left\{ \matrix{
a > b > c \hfill \cr
a + b + c = 54\,\,\,\,\,\, \hfill \cr} \right.\,\,\,\,;\,\,\,\,\,\,\,\,\,\,?\,\, = \,\,a$$

Let´s start with statement (2) not only because it´s easier, but also because it will help us finding (uniqueness or) a BIFURCATION of the other statement!

$$\left( 2 \right)\,\,\,b + c = 30\,\,\,\,\, \Rightarrow \,\,\,\,\,? = a = 54 - 30 = 24\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$

$$\left( 1 \right)\,\,a = 2c\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {24,18,12} \right)\,\,\,\,\, \Rightarrow \,\,\,\,a = 24\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {26,15,13} \right)\,\,\,\,\, \Rightarrow \,\,\,\,a = 26\,\, \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Jay@ManhattanReview » Mon Nov 05, 2018 12:04 am

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BTGmoderatorLU wrote:Source: GMAT Prep

If the sum of the three different numbers is 54, what is the largest number?

1) The largest number is twice the smallest number.
2) The sum of the two smaller numbers is 30.

The OA is B.
Say the three different numbers are a, b and c such that a > b > c.

Question: What's the value of c?

We have a + b + c = 54.

Let's take each statement one by one.

1) The largest number is twice the smallest number.

=> c = 2a

Thus, a + b + c = 54 => a + b + 2a = 54 => 3a + b = 54. Can't get the unique value of a, thus, c. Insufficient.

2) The sum of the two smaller numbers is 30.

=> a + b = 30.

From a + b + c = 54, we have 30 + c = 54 => c = 24. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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