If Q is an integer between 10 and 100, what is the value of

If Q is an integer between 10 and 100, what is the value of Q?

(1) One of Q's digits is 3 more than the other, and the sum of its digits is 9.
(2) Q< 50


Given: \(10 < Q <100\)

Statement (1)

Let \(x\) and \(y\) be the digits of \(Q\)

As per statement (1),\(x + y =9\) and either \(x = y + 3\) or \(y = x +3\)

Solving, \(x\) and \(y\) are \(3, 6\) or \(6, 3\) or Q is \(36\) o r\(63.\)
As \(Q\) can not be determined uniquely, the statement(1) is not sufficient...... Option (A) & (D)

Statement (2)

\(10 < Q < 50\)

Or, Q can assume any value between 11 and 49 (11 & 49 inclusive),
Thus, Q can not be uniquely determined, not sufficient............................Option(B)

Combining both statements (1) and (2), Q is equal to 36.........................Option(E)

Answer: (C)

1, Q's digits 3 more than other
3+6 = 9 ; Q = 36
6 + 3 = 9 ; Q = 63
Insufficient
2, Q < 50 Insufficient
3, Only 1 value
C

We are given that Q is an integer between 10 and 100, and we must determine the value of Q.

Statement One Alone:

One of Q's digits is 3 more than the other, and the sum of its digits is 9.

Statement one alone is not sufficient to answer the question. If we let A = the tens digit and B = the units digit, then we can create the following equations:

A + B = 9

A = B + 3 (keep in mind that this can be reversed)

B + 3 + B = 9

2B = 6

B = 3

Thus, A = 6

So Q could be 36 or 63. Statement one is not sufficient to answer the question.

Statement Two Alone:

Q < 50

Only knowing that Q is less than 50 is not enough information to answer the question. Thus, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From statement one, we see that Q is either 36 or 63. From statement two, Q < 50. So Q must be 36 to satisfy both statements. The two statements together are sufficient to answer the question.

Answer: C

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