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05 Nov 2018, 00:21
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Difficulty:
65%
(hard)
Question Stats:
47% (01:41) correct
53%
(01:59)
wrong
based on 109
sessions
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If x and y are positive integers and y^2 = 9 − x, what is the value of y?
(1) x ≤ 7
(2) y ≥ 2
(1) x ≤ 7
(2) y ≥ 2
05 Nov 2018, 02:17
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Starting with y=1, and moving on up, we'll find the only positive integers x,y for which the equation works: y=1, x=8 (1=9-8), and y=2, x = 5 (4=6-5). for y=3 we get x=0 (9=9-0), which is out of range, and for any larger y value we'll get a negative x - out of range.
1) eliminates the option of y=1, x=8, leaving only y=2,x=5. Sufficient!
2) eliminates y=1, x=8, leaving only y=2,x=5. Sufficient!
Answer D.
1) eliminates the option of y=1, x=8, leaving only y=2,x=5. Sufficient!
2) eliminates y=1, x=8, leaving only y=2,x=5. Sufficient!
Answer D.
05 Nov 2018, 02:28
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Lets understand the question:
Given X and Y is a positive integer. So, Y^2 has to be a integer.
So value of 9-X has to be a perfect square. ( x is a positive integer so it cant be zero)
Statement 1)
x ≤ 7, only value satisfy for y to be integer is x=5 or zero, but x cant be zero.
Hence x=5 and y =2. Sufficient.
Statement 2)
y ≥ 2
again x cant be greater than 9 and cant be zero, so only possible value of y is 2
which gives y^2= 9-X a positive integer.
Sufficient
Answer D.
Given X and Y is a positive integer. So, Y^2 has to be a integer.
So value of 9-X has to be a perfect square. ( x is a positive integer so it cant be zero)
Statement 1)
x ≤ 7, only value satisfy for y to be integer is x=5 or zero, but x cant be zero.
Hence x=5 and y =2. Sufficient.
Statement 2)
y ≥ 2
again x cant be greater than 9 and cant be zero, so only possible value of y is 2
which gives y^2= 9-X a positive integer.
Sufficient
Answer D.
