x is a two-digit integer and y is a three-digit integer that

[BTGmoderatorDC]

x is a two-digit integer and y is a three-digit integer that is divisible by x. If z is the value of the quotient y/x, is the units digit of z greater than 3?

(1) The units digit of x is 3.
(2) The units digit of y is the same as the units digit of x.

OA C

Source: Veritas Prep

[Jay@ManhattanReview]

x is a two-digit integer and y is a three-digit integer that is divisible by x. If z is the value of the quotient y/x, is the units digit of z greater than 3?

(1) The units digit of x is 3.
(2) The units digit of y is the same as the units digit of x.

OA C

Source: Veritas Prep

Given: x is a two-digit integer and y is a three-digit integer that is divisible by x, and z is the value of the quotient y/x.

Question: Is the units digit of z greater than 3?

Let's take each statement one by one.

(1) The units digit of x is 3.

We have no information about y. Insufficient.

Say y = 230 and x = 23, then y/x = 10 => z = 0 < 3. However, if say y = 138 and x = 23, then y/x = 6 => z = 6 > 3. No unique answer. Insufficient.

(2) The units digit of y is the same as the units digit of x.

Say say y = 120 and x = 20, then z = y/x = 6 => Units digit of z = 6 > 3. However, if say y = 110 and x = 10, then z = y/x = 11 => Units digit of z = 1 < 3. No unique answer. Insufficient.

(1) and (2) together

Say y = ab3 and x = p3 => y/x = z = ab3/p3

=> ab3 = p3 * z

Thus, we must have units digit of 3z = 3; this is possible only if the units digit of z equals 1. The answer is No. A unique answer. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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