A number A is a two-digit positive.....FDP 5th ed

[bmshah1]

I am wondering if somebody can help me understand the rationale behind the correct answer for this DS problem (located on pg 119 MGMAT Guide1 5th Ed.):

The number A is a two-digit positive integer; the number B is the two-digit positive integer formed by reversing the digits of A. If Q = 10B-A, what is the value of Q?

1) The tens digit of A is 7.
2) The tens digit of B is 6.

I am wondering:
1) Why B and "not A" is the answer.
2) What would be the answer if the equation was changed to Q = 10A-B.

Statement 1 indicates that 7 is located in the tens digit of A so in theory you can come up with a number from 70...79 that will allow you to know the value of B as per the requirement in the statement and in turn calculate the value of Q (I am seeing the equation as Q = (10*B) - A).

On the other hand I thought for statement 2 we know the value of B (60...69) but we would not be able to know the value of A (as the statement doesn't indicate that you can reverse the digits of B to determine the value of A). So in my mind I am thinking A as the answer.

BTW the official answer does make sense but I am wondering where am I going wrong.

[divineacclivity]

hey,

Since A is a 2-digit number, let's say x is at tens' place and y at unit's, so, the number A can be written as: 10x+y
=> A = 10x + y
Since B is reverse of A => B = 10y + x

Q = 10 B - A
= 10 (10y + x) - (10x + y)
= 100y + 10x - 10x -y
= 99y
and y is unit's digit of A and tens' of B => Answer is B alone

Hope this helps

[bmshah1]

hey,

Since A is a 2-digit number, let's say x is at tens' place and y at unit's, so, the number A can be written as: 10x+y
=> A = 10x + y
Since B is reverse of A => B = 10y + x

Q = 10 B - A
= 10 (10y + x) - (10x + y)
= 100y + 10x - 10x -y
= 99y
and y is unit's digit of A and tens' of B => Answer is B alone

Hope this helps

I saw that in the official explanation but it still doesn't clear my confusion that I have made in my original post. If Statement 1 says tens digit of A is 7 then I can make a value of A say 71 then B would be 17 and Q can be easily calculated.

[jlucero]

hey,

Since A is a 2-digit number, let's say x is at tens' place and y at unit's, so, the number A can be written as: 10x+y
=> A = 10x + y
Since B is reverse of A => B = 10y + x

Q = 10 B - A
= 10 (10y + x) - (10x + y)
= 100y + 10x - 10x -y
= 99y
and y is unit's digit of A and tens' of B => Answer is B alone

Hope this helps

I saw that in the official explanation but it still doesn't clear my confusion that I have made in my original post. If Statement 1 says tens digit of A is 7 then I can make a value of A say 71 then B would be 17 and Q can be easily calculated.

I think you are misunderstanding the data sufficiency aspect of this question. You can calculate Q if you know exactly what A or B is. But test out these two examples:

If A = 71 and B = 17, then Q = -71
If A = 72 and B = 27, then Q = 198

This is why (1) is insufficient. Not because we don't know exactly what A or B is, but because Q could be different answers. On the other hand, if we take statement (2):

If B = 61 and A = 16, then Q = 594
If B = 62 and A = 26, then Q = 594
...
If B = 69 and A = 96, then Q = 594

Algebraically, this is divineacclivity proved. That we can break down the equation Q = 10 B - A to Q = 99y, where we only need to know the value of the tens digit of B.

If you were to switch the equation to Q = 10 B - A, then the algebraic solution would change to Q = 99x, and yes, the answer would change to (A).

[bmshah1]

hey,

Since A is a 2-digit number, let's say x is at tens' place and y at unit's, so, the number A can be written as: 10x+y
=> A = 10x + y
Since B is reverse of A => B = 10y + x

Q = 10 B - A
= 10 (10y + x) - (10x + y)
= 100y + 10x - 10x -y
= 99y
and y is unit's digit of A and tens' of B => Answer is B alone

Hope this helps

I saw that in the official explanation but it still doesn't clear my confusion that I have made in my original post. If Statement 1 says tens digit of A is 7 then I can make a value of A say 71 then B would be 17 and Q can be easily calculated.

I think you are misunderstanding the data sufficiency aspect of this question. You can calculate Q if you know exactly what A or B is. But test out these two examples:

If A = 71 and B = 17, then Q = -71
If A = 72 and B = 27, then Q = 198

This is why (1) is insufficient. Not because we don't know exactly what A or B is, but because Q could be different answers. On the other hand, if we take statement (2):

If B = 61 and A = 16, then Q = 594
If B = 62 and A = 26, then Q = 594
...
If B = 69 and A = 96, then Q = 594

Algebraically, this is divineacclivity proved. That we can break down the equation Q = 10 B - A to Q = 99y, where we only need to know the value of the tens digit of B.

If you were to switch the equation to Q = 10 B - A, then the algebraic solution would change to Q = 99x, and yes, the answer would change to (A).

Thanks Joe....that clears the confusion.

[divineacclivity]

hey,

Since A is a 2-digit number, let's say x is at tens' place and y at unit's, so, the number A can be written as: 10x+y
=> A = 10x + y
Since B is reverse of A => B = 10y + x

Q = 10 B - A
= 10 (10y + x) - (10x + y)
= 100y + 10x - 10x -y
= 99y
and y is unit's digit of A and tens' of B => Answer is B alone

Hope this helps

I saw that in the official explanation but it still doesn't clear my confusion that I have made in my original post. If Statement 1 says tens digit of A is 7 then I can make a value of A say 71 then B would be 17 and Q can be easily calculated.

Oh, ok. I didn't look it up from OG or any other source. But I'm glad to hear I was thinking on the same lines & I'm glad that your issue is resolved.

[tim]

please let us know if there are any further questions about this one..

[NIBA]

Hi,

I applied the 'algebraic' method and could arrive at the answer 'B'.

But, say if I do not want to use the algebraic method and want to answer with the information provided i.e, taking both the statements into consideration and I come to conclusion that both statements are required to get the correct answer - 'C'.

1.As per this statement I can conclude that A = 7Y
2.As per this statement I can conclude that B = 6X.

Taking both the statements into consideration:

A = 76
B = 67

Therefore Q = 10*67-76 = 670-76= 594.

Then I get the answer as 'C'. Please help?

[tim]

This is a common pitfall. Remember that you have to *fully* analyze each statement separately to see if it works *before* combining them to see if they work together. Just because the statements in conjunction will answer the question does not mean the answer is C. In fact, on *every* question for which A, B, or D is the answer, the statements combined will be sufficient. Remember though that A, B, and D trump C in this regard if either (or both) of the statements is sufficient on its own.