Mo2men wrote:x/y=5.35 and If x and y are positive integers, then what is the value of x?
(1) When y is divided by x, the remainder is 20.
(2) When x is divided by y, the remainder is 7.
OA: D
Source: Economist
We are given that x/y = 5.35 and x and y are positive integers.
We have to determine the value of x.
x/y = 5.35 => x/y = 535/100 = 107/20; after cancelling 535 and 100 by 5.
=> 107 and 20 would be the multiples of the same common factor.
Say the common factor is n, then we have x/y = (107n) / (20n).
If we get the value of n, we would get the value of x = 107n.
Let's take each statement one by one.
(1) When y is divided by x, the remainder is 20.
=> y = xq + 20
=> 20n = (107n)q + 20; where q is the quotient
=> n(20 - 107q) = 20
Since n is postive quality, (20 - 107q) must be positive. Since q is a non-negative integer, q = 0.
=> n*(20 - 0) = 20 => 20n = 20 => n = 1.
Thus, x = 107n = 107*1 = 107. Sufficient.
(2) When x is divided by y, the remainder is 7.
=> 107n = (20n)q + 7
=> n(107 - 20q) = 7
We see that 7, a prime number, is a product of two positive integers n and (107 - 20q).
Thus, one between n and (107 - 20q) should be 1 and the other 7,
Case 1: Say n = 7 and 107 - 20q = 1 => q = 106/20 = fraction. It's not possible as q is an integer.
Case 2: Say n = 1 and 107 - 20q = 7 => q = 100/20 = 5. It's possible as q is an integer.
=> n = 1.
Thus, x = 107n = 107*1 = 107. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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