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Senior Manager  Joined: 13 Jan 2012
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If the sum of the three different numbers is 54, what is the largest  [#permalink]

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Question Stats: 69% (01:11) correct 31% (01:37) wrong based on 293 sessions

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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?
Current Student Joined: 08 Jan 2009
Posts: 291
GMAT 1: 770 Q50 V46 Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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

2x = 24
y = 18
x = 12

2x = 22
y = 21
x = 11

NS
Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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2
2
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.[/textarea]

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?

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

Given: $$x<y<z$$ and $$x+y+z=54$$.
Question: $$z=?$$

(1) The largest number is twice the smallest number --> $$x+y+2x=54$$ --> $$3x+y=54$$. Now we should find $$x$$ so that $$x<y$$ and $$3x+y=54$$:
$$x=11$$, $$y=21$$, $$z=22$$;
$$x=12$$, $$y=18$$, $$z=24$$;
$$x=13$$, $$y=15$$, $$z=26$$;

Also notice that we are not told that unknowns represent integers only so non-integer values are also valid. For example: $$x=12.5$$, $$y=16.5$$, and $$z=25$$.
Not sufficient.

(2) The sum of the two smaller numbers is 30 --> x+y=30 --> $$30+z=54$$ --> z=24. Sufficient.

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Posts: 65
Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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Bunuel wrote:
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.[/textarea]

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?

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

Given: $$x<y<z$$ and $$x+y+z=54$$.
Question: $$z=?$$

(1) The largest number is twice the smallest number --> $$x+y+2x=54$$ --> $$3x+y=54$$. Now we should find $$x$$ so that $$x<y$$ and $$3x+y=54$$:
$$x=11$$, $$y=21$$, $$z=22$$;
$$x=12$$, $$y=18$$, $$z=24$$;
$$x=13$$, $$y=15$$, $$z=26$$;

Also notice that we are not told that unknowns represent integers only so non-integer values are also valid. For example: $$x=12.5$$, $$y=16.5$$, and $$z=25$$.
Not sufficient.

(2) The sum of the two smaller numbers is 30 --> x+y=30 --> $$30+z=54$$ --> z=24. Sufficient.

How do we know z is largest
Math Expert V
Joined: 02 Aug 2009
Posts: 7954
Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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sagnik242 wrote:
Bunuel wrote:
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.[/textarea]

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?

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

Given: $$x<y<z$$ and $$x+y+z=54$$.
Question: $$z=?$$

(1) The largest number is twice the smallest number --> $$x+y+2x=54$$ --> $$3x+y=54$$. Now we should find $$x$$ so that $$x<y$$ and $$3x+y=54$$:
$$x=11$$, $$y=21$$, $$z=22$$;
$$x=12$$, $$y=18$$, $$z=24$$;
$$x=13$$, $$y=15$$, $$z=26$$;

Also notice that we are not told that unknowns represent integers only so non-integer values are also valid. For example: $$x=12.5$$, $$y=16.5$$, and $$z=25$$.
Not sufficient.

(2) The sum of the two smaller numbers is 30 --> x+y=30 --> $$30+z=54$$ --> z=24. Sufficient.

How do we know z is largest

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
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Intern  Joined: 21 Jul 2013
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GMAT 1: 690 Q48 V35 Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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Bunuel wrote:
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.[/textarea]

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?

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

Given: $$x<y<z$$ and $$x+y+z=54$$.
Question: $$z=?$$

(1) The largest number is twice the smallest number --> $$x+y+2x=54$$ --> $$3x+y=54$$. Now we should find $$x$$ so that $$x<y$$ and $$3x+y=54$$:
$$x=11$$, $$y=21$$, $$z=22$$;
$$x=12$$, $$y=18$$, $$z=24$$;
$$x=13$$, $$y=15$$, $$z=26$$;

Also notice that we are not told that unknowns represent integers only so non-integer values are also valid. For example: $$x=12.5$$, $$y=16.5$$, and $$z=25$$.
Not sufficient.

(2) The sum of the two smaller numbers is 30 --> x+y=30 --> $$30+z=54$$ --> z=24. Sufficient.

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.
Math Expert V
Joined: 02 Aug 2009
Posts: 7954
Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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FasuSek wrote:
Bunuel wrote:
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.[/textarea]

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?

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

Given: $$x<y<z$$ and $$x+y+z=54$$.
Question: $$z=?$$

(1) The largest number is twice the smallest number --> $$x+y+2x=54$$ --> $$3x+y=54$$. Now we should find $$x$$ so that $$x<y$$ and $$3x+y=54$$:
$$x=11$$, $$y=21$$, $$z=22$$;
$$x=12$$, $$y=18$$, $$z=24$$;
$$x=13$$, $$y=15$$, $$z=26$$;

Also notice that we are not told that unknowns represent integers only so non-integer values are also valid. For example: $$x=12.5$$, $$y=16.5$$, and $$z=25$$.
Not sufficient.

(2) The sum of the two smaller numbers is 30 --> x+y=30 --> $$30+z=54$$ --> z=24. Sufficient.

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.

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
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Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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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.
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Re: If the sum of the three different numbers is 54, what is the largest  [#permalink]

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geometric wrote:
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,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net Re: If the sum of the three different numbers is 54, what is the largest   [#permalink] 02 Nov 2018, 16:16
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