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![How many integer solutions does the equation [m][square_root]x[/square](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "How many integer solutions does the equation [m][square_root]x[/square"){kind=icon}
02 Feb 2021, 09:09
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (01:51) correct
69%
(02:00)
wrong
based on 80
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How many integer solutions does the equation \(\sqrt{x}+\sqrt{y}=1984 \) have?
A. 0
B. 1
C. 24
D. 1984
E. 1985
A. 0
B. 1
C. 24
D. 1984
E. 1985
02 Feb 2021, 19:31
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gmatcafe
Now both x and y have to be positive integers.
\(\sqrt{x}+\sqrt{y}=1984 \)
Now 1984=0+1984=1+1983=2+1982=....=1983+1=1984+0
So the values of \(\sqrt{x} \ \ and \ \ \sqrt{y} \ \ can \ \ be \ \{0,1984};{1,1983}.... \)
Total values of \(\sqrt{x}\) will be from 0 to 1984, so total 1985 and for each of these there is a value for \(\sqrt{y}\)
These 1985 values when calculated for {x,y} will be \((0,1984^2);(1,1983^2)...\)
E
29 Apr 2021, 22:12
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Hmm, shouldn’t the order matter or are we looking for unordered solutions?
What I mean is:
Solution 1: x = (1984)^2 and y = 0
is a different solution from
Solution 2: x = 0 and y = (1984)^2
The answer has to be E, but technically speaking for the future, what are your thoughts chetan2u ?
Thank you much
Edit: or am I already thinking too far beyond the GMAT in terms of ordered vs. unordered solutions.
Posted from my mobile device
What I mean is:
Solution 1: x = (1984)^2 and y = 0
is a different solution from
Solution 2: x = 0 and y = (1984)^2
The answer has to be E, but technically speaking for the future, what are your thoughts chetan2u ?
Thank you much
Edit: or am I already thinking too far beyond the GMAT in terms of ordered vs. unordered solutions.
Posted from my mobile device
