Last visit was: 27 Apr 2026, 07:40 It is currently 27 Apr 2026, 07:40
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
505-555 (Easy)|   Algebra|      
User avatar
geometric
User avatar
Joined: 13 Jan 2012
Last visit: 15 Feb 2017
Posts: 243
Own Kudos:
907
 [42]
Given Kudos: 38
Weight: 170lbs
GMAT 1: 740 Q48 V42
GMAT 2: 760 Q50 V42
WE:Analyst (Other)
GMAT 2: 760 Q50 V42
Posts: 243
Kudos: 907
 [42]
If the sum of the three different numbers is 54, what is the largest 15 Jan 2012, 23:50
4
Kudos
Add Kudos
38
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

76% (01:12) correct 24% (01:29) wrong based on 1442 sessions

History

Date
Time
Result
Not Attempted Yet
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.

Show Spoiler
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?
ShowHide Answer
Official Answer
B
If this question felt shaky, try an adaptive mini quiz of similar problems in GMAT Club Forum Quiz →. Free plan gives 5 questions per day.
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,928
Own Kudos:
811,556
 [8]
Given Kudos: 105,914
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,928
Kudos: 811,556
 [8]
If the sum of the three different numbers is 54, what is the largest 16 Jan 2012, 03:38
4
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
vandygrad11
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]

Show Spoiler
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?
Show more

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.

Answer: B.
General Discussion
User avatar
pike
User avatar
Current Student
Joined: 08 Jan 2009
Last visit: 27 Dec 2020
Posts: 245
Own Kudos:
505
 [3]
Given Kudos: 7
GMAT 1: 770 Q50 V46
GMAT 1: 770 Q50 V46
Posts: 245
Kudos: 505
 [3]
If the sum of the three different numbers is 54, what is the largest 16 Jan 2012, 00:13
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
1)
2x + y + x = 54
3x + y = 54

2x = 24
y = 18
x = 12

2x = 22
y = 21
x = 11

NS
User avatar
sagnik242
User avatar
Joined: 28 Dec 2013
Last visit: 04 Oct 2016
Posts: 47
Own Kudos:
14
 [1]
Given Kudos: 3
Posts: 47
Kudos: 14
 [1]
If the sum of the three different numbers is 54, what is the largest 23 Dec 2015, 15:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
vandygrad11
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]

Show Spoiler
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.

Answer: B.
Show more
How do we know z is largest
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 27 Apr 2026
Posts: 11,229
Own Kudos:
45,028
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,028
If the sum of the three different numbers is 54, what is the largest 23 Dec 2015, 18:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sagnik242
Bunuel
vandygrad11
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]

Show Spoiler
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.

Answer: B.
How do we know z is largest
Show more

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
avatar
FasuSek
avatar
Joined: 21 Jul 2013
Last visit: 16 May 2017
Posts: 1
Given Kudos: 3
GMAT 1: 690 Q48 V35
Products:
My Reviews
GMAT 1: 690 Q48 V35
Posts: 1
Kudos: 0
If the sum of the three different numbers is 54, what is the largest 17 Feb 2016, 19:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
vandygrad11
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]

Show Spoiler
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.

Answer: B.
Show more


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.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 27 Apr 2026
Posts: 11,229
Own Kudos:
45,028
 [3]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,028
 [3]
If the sum of the three different numbers is 54, what is the largest 17 Feb 2016, 19:23
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
FasuSek
Bunuel
vandygrad11
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]

Show Spoiler
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.

Answer: B.


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.
Show more

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
User avatar
anairamitch1804
User avatar
Joined: 26 Oct 2016
Last visit: 20 Apr 2019
Posts: 502
Own Kudos:
3,606
 [1]
Given Kudos: 877
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE:Education (Education)
Schools: HBS '19
GMAT 1: 770 Q51 V44
Posts: 502
Kudos: 3,606
 [1]
If the sum of the three different numbers is 54, what is the largest 26 Jan 2017, 22:17
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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.
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,889
 [1]
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,889
 [1]
If the sum of the three different numbers is 54, what is the largest 02 Nov 2018, 16:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
geometric
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.
Show more
\(\left\{ \matrix{\\
a > b > c \hfill \cr \\
a + b + c = 54\,\,\,\,\,\, \hfill \cr} \right.\,\,\,\,;\,\,\,\,\,\,\,\,\,\,?\,\, = \,\,a\)

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.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,988
Own Kudos:
1,118
Posts: 38,988
Kudos: 1,118
If the sum of the three different numbers is 54, what is the largest 24 Apr 2025, 01:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109928 posts
kingbucky
498 posts
Gmat860sanskar
212 posts