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

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

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15 Jan 2012, 22:50
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69% (00:43) correct 31% (01:00) wrong based on 365 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?
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Re: If the sum of the three different numbers is 54, what is the  [#permalink]

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15 Jan 2012, 23:13
1)
2x + y + x = 54
3x + y = 54

2x = 24
y = 18
x = 12

2x = 22
y = 21
x = 11

NS
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Posts: 50627
Re: If the sum of the three different numbers is 54, what is the  [#permalink]

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16 Jan 2012, 02:38
2
1
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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Re: If the sum of the three different numbers is 54, what is the  [#permalink]

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22 May 2013, 02:40
Bumping for review and further discussion.
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Re: If the sum of the three different numbers is 54, what is the  [#permalink]

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23 Dec 2015, 14:39
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
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Joined: 02 Aug 2009
Posts: 7037
Re: If the sum of the three different numbers is 54, what is the  [#permalink]

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23 Dec 2015, 17:29
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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

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17 Feb 2016, 18:12
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
Joined: 02 Aug 2009
Posts: 7037
Re: If the sum of the three different numbers is 54, what is the  [#permalink]

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17 Feb 2016, 18:23
3
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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

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26 Jan 2017, 21:17
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.
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Re: If the sum of the three different numbers is 54, what is the  [#permalink]

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02 Nov 2018, 15:16
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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Re: If the sum of the three different numbers is 54, what is the &nbs [#permalink] 02 Nov 2018, 15:16
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