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

Question

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

Bunuel · Answer

SOLUTION

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. Both 36 and 63 satisfy this statement. Not sufficient.

(2) Q < 50. Not sufficient.

(1)+(2) Since Q is less than 50, then Q = 36. Sufficient.

Answer: C.

kinjiGC · Answer

If the number is between 10 and 100, the number has to be 2 digit number.

Statement 1) Let the number be XY, so X-Y = 3 and X+Y = 9, So numbers possible are 63 or 36. Not Sufficient.

Statement 2) Q < 50. So many numbers are possible. Not Sufficient.

Combining the two statement, only one number possible which is 36. Hence Option C)

arunspanda · Answer

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)

kanusha · Answer

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

JeffTargetTestPrep · Answer

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

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards