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20 Apr 2020, 02:42
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Difficulty:
45%
(medium)
Question Stats:
63% (01:33) correct
37%
(01:37)
wrong
based on 218
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If x and y are positive integers, what is the result when the units digit of \((5x − 3)6 + y\) is divided by 10 ?
(1) \(y = 4\)
(2) \(x = 5\)
20 Apr 2020, 03:29
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Known: x and y are positive integers
Q. Remainder of (5x-3)*6 + y when divided by 10
1) y=4
For any x-value, (5*x-3)*6 always has a unit digit of 2. If y=4, then { (5*x-3)*6 +y } has unit digit of 6 when divided by 10. So, the result is 6.
SUFFICIENT
2) x=5
We only know that (5*5-3)*6 has unit digit of 2. Since we know nothing about y-value, we cannot deduce the exact result when the units digit of { (5x-3)*6 +y } is divided by 10.
NOT SUFFICIENT
FINAL ANSWER IS (A)
Posted from my mobile device
Q. Remainder of (5x-3)*6 + y when divided by 10
1) y=4
For any x-value, (5*x-3)*6 always has a unit digit of 2. If y=4, then { (5*x-3)*6 +y } has unit digit of 6 when divided by 10. So, the result is 6.
SUFFICIENT
2) x=5
We only know that (5*5-3)*6 has unit digit of 2. Since we know nothing about y-value, we cannot deduce the exact result when the units digit of { (5x-3)*6 +y } is divided by 10.
NOT SUFFICIENT
FINAL ANSWER IS (A)
Posted from my mobile device
20 Apr 2020, 04:03
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We re given that \(x\) and \(y\) are positive integers and asked to find the remainder when \((5x-3)*6+y\) is divided by \(10\)
\((5x-3)*6+y=(30x+y-18)\)
We are to find the remainder of \(\frac{(30x+y-18)}{10} =\) the remainder of \(\frac{30x}{10} +\) the remainder of \(\frac{(y-18)}{10} = 0+\) the remainder of \(\frac{(y-18)}{10}\)
Hence we only need the value of \(y\).
Statement 1: y=4
Sufficient. Since we determine the remainder to be -4 = 6.
Statement 2: x=15
The value of x is not necessary. What we need is the value of y.
the answer is A.
\((5x-3)*6+y=(30x+y-18)\)
We are to find the remainder of \(\frac{(30x+y-18)}{10} =\) the remainder of \(\frac{30x}{10} +\) the remainder of \(\frac{(y-18)}{10} = 0+\) the remainder of \(\frac{(y-18)}{10}\)
Hence we only need the value of \(y\).
Statement 1: y=4
Sufficient. Since we determine the remainder to be -4 = 6.
Statement 2: x=15
The value of x is not necessary. What we need is the value of y.
the answer is A.
