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

Question

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.

Here, the answer is B (statement 2 alone). I don't see why statement 1 is insufficient. If the largest number is twice the smallest number, doesn't that lead only to 12 and 24 for those two numbers and 18 for the middle number?

Bunuel · Accepted Answer

If the sum of the three different numbers is 54, what is the largest number? Given: x x+y+2x=54 --> 3x+y=54 . Now we should find x so that x x+y=30 --> 30+z=54 --> z=24. Sufficient. Answer: B.

pike · Answer

1) 
2x + y + x = 54
3x + y = 54

2x = 24
y = 18
x = 12

2x = 22
y = 21
x = 11

NS

sagnik242 · Answer

How do we know z is largest

chetan2u · Answer

Hi,

the statement tells us that 30 is the sum of two smallest numbers..
so the remaining difference will have to be the third number, which will be the largest

FasuSek · Answer

From Statement 2 how do we know that x is not 29 and y=1, or x=28 and y=2?
In those cases x would be the largest number.

chetan2u · Answer

Hi,
the answer lies within the statement 2 itself..
 (2) The sum of the two smaller numbers is 30

now this tells us that 30 is the sum of two smaller numbers..
so x cannot be 28 or 29 it has to be less than the largest number 54-30=24.. 
hope it helps

anairamitch1804 · Answer

When you modify the original condition and the question, based on a<b<c, you only need to know a+b 
from 1) a+b+c=54, c=54-(a+b). 
Since 2) a+b=30, c=54-30=24, 
which is unique and sufficient. 
Therefore the answer is B.

fskilnik · Answer

\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, 
Fabio.

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

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

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