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655-705 Level|   Algebra|         
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adityaprateek15
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GMAT Club Olympics 2025 (Day 9): If the positive difference of the 11 Jul 2025, 08:59
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Hello bb, Bunuel Could you please validate this and reward kudos if this qualifies? Thanks
adityaprateek15
Let the two integers be a and b
Given,
|√a - √b| = √15-10√2
Squaring both sides
a + b - 2√ab = 15 - 10√2
Comparing LHS with RHS, we get:
2√ab = 10√2
√ab = 5√2
√ab = √25*2
√ab = √50 and
a + b = 15
which means
a=10 and b=5
or a=5 and b=10
Q: (a-b)^2
(10-5)^2 or (5-10)^2
5^2 or (-5)^2
Both equals 25.

Option C

Bunuel
If the positive difference of the square roots of two integers is \(\sqrt{15 - 10\sqrt{2}}\), what is the square of the difference between these two integers?

A. 9
B. 16
C. 25
D. 100
E. 225


 


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for the GMAT Club Olympics Competition

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svsivakrishna
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GMAT Club Olympics 2025 (Day 9): If the positive difference of the 11 Jul 2025, 09:39
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The question created lot of confusion as the first square root shown before 15 is not extending for the complete value.
It would have been better if it were representated as sqrt (15-10*sqrt(2))
Since there was no paranthesis, I wasted a lot of time trying to solve the question.
Bunuel
If the positive difference of the square roots of two integers is \(\sqrt{15 - 10\sqrt{2}}\), what is the square of the difference between these two integers?

A. 9
B. 16
C. 25
D. 100
E. 225


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

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Bunuel
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GMAT Club Olympics 2025 (Day 9): If the positive difference of the 11 Jul 2025, 14:47
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svsivakrishna
The question created lot of confusion as the first square root shown before 15 is not extending for the complete value.
It would have been better if it were representated as sqrt (15-10*sqrt(2))
Since there was no paranthesis, I wasted a lot of time trying to solve the question.
Bunuel
If the positive difference of the square roots of two integers is \(\sqrt{15 - 10\sqrt{2}}\), what is the square of the difference between these two integers?

A. 9
B. 16
C. 25
D. 100
E. 225


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more

It covers the entire expression under it:



Does it show something else on your screen?
Show Spoiler
Attachment:
GMAT-Club-Forum-s7vf9kq9.png
GMAT-Club-Forum-s7vf9kq9.png [ 8.01 KiB | Viewed 193 times ]
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svsivakrishna
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GMAT Club Olympics 2025 (Day 9): If the positive difference of the 11 Jul 2025, 21:50
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Hi

Bunuel
Thank you for the reply.

I am unable to attach any file in the reply due to permission restrictions.

Please let me know if there is any way to send you the screenshot of the question display at my end.

The square root is showing only for the value 15. ( Brave browser, Mac OS)
Bunuel
svsivakrishna
The question created lot of confusion as the first square root shown before 15 is not extending for the complete value.
It would have been better if it were representated as sqrt (15-10*sqrt(2))
Since there was no paranthesis, I wasted a lot of time trying to solve the question.
Bunuel
If the positive difference of the square roots of two integers is \(\sqrt{15 - 10\sqrt{2}}\), what is the square of the difference between these two integers?

A. 9
B. 16
C. 25
D. 100
E. 225


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


It covers the entire expression under it:



Does it show something else on your screen?
Show Spoiler
Attachment:
GMAT-Club-Forum-s7vf9kq9.png
Show more
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Bunuel
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778,068
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Posts: 105,355
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GMAT Club Olympics 2025 (Day 9): If the positive difference of the 11 Jul 2025, 23:07
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svsivakrishna
Hi

Bunuel
Thank you for the reply.

I am unable to attach any file in the reply due to permission restrictions.

Please let me know if there is any way to send you the screenshot of the question display at my end.


Show more

You can pm me the file.
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