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31 Aug 2021, 21:47
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B
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:
39% (02:52) correct
61%
(02:48)
wrong
based on 102
sessions
History
Date
Time
Result
Not Attempted Yet
The number of pairs of integers(x,y) satisfying x ≥ y ≥ -20 and 2x + 5y = 99 is
A 12
B 17
C 18
D 20
E 9
A 12
B 17
C 18
D 20
E 9
01 Sep 2021, 02:52
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sarthakaggarwal
\(2x+5y=99\)
We ca say that u has to be ODD, as x will not be an integer otherwise.
With every change of 2 in y, there will be a change of 5 in y.
For example
When y=11, x=22.
When y=13, x=17
So y=15 will result in lower value of x 17-5 or 12
Thus, our answer is all odd values between -20 and 14.
So \(\frac{14-(-20)}{2}=17\)
B
01 Sep 2021, 07:11
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sarthakaggarwal
Since 2x is even and 99 is odd, we can confirm 5y has to be odd. Then y has to be odd. We may start with \(y = -19\) and increase y until we hit x ≥ y. We don't really need to care about the values of x, it must be an integer since 2x can be any even number.
If we plug in x = y, then we have 7y = 99 and y is roughly 14. Then we largest y we can take is y = 13. Again we can only take odd y's.
Then then number of y's is: \(\frac{13 - (-19)}{2} + 1 = 16 + 1 = 17\).
Ans: B
