beyondenim wrote:Data Sufficiency: 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 = lOB - A, what is the value of Q?

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

Hi not able to understand this "Q = lOB - A" is it? Q = l0B - A after 1 is it 0 (zero) and then B?

A = 10X + Y
B = 10Y + X

10B-A = 10(10Y + X) - 10X - Y

= 99Y.

We need to find Y and statement 2 gives us that. Hence B

shankar.ashwin wrote:A = 10X + Y
B = 10Y + X

10B-A = 10(10Y + X) - 10X - Y

= 99Y.

We need to find Y and statement 2 gives us that. Hence B

Lets say A = xy ( a two digit number ) = 10x+y
Then B = yx = 10y+x
Now the given equation is Q = 10B - A
= 100+B-A
=100 + 10y + x - 10x - y
= 100 + 9 (y - x)
So we can find the value of Q only if u have the value of both x and y which are the tens digit of A ( ie x) and the tens digit of B ( ie y)
So answer is C

I think we cannot write 10B = 10 * B ....
Ex: 103 = 10 * 3 ????????
Hope i am clear..........
By the way whats the answer?????
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If iam WRONG please correct me, if i am correct and cleared your doubt Thank me

nandy1984 wrote:

shankar.ashwin wrote:A = 10X + Y
B = 10Y + X

10B-A = 10(10Y + X) - 10X - Y

= 99Y.

We need to find Y and statement 2 gives us that. Hence B

Lets say A = xy ( a two digit number ) = 10x+y
Then B = yx = 10y+x
Now the given equation is Q = 10B - A
= 100+B-A
=100 + 10y + x - 10x - y
= 100 + 9 (y - x)
So we can find the value of Q only if u have the value of both x and y which are the tens digit of A ( ie x) and the tens digit of B ( ie y)
So answer is C

I think we cannot write 10B = 10 * B ....
Ex: 103 = 10 * 3 ????????
Hope i am clear..........
By the way whats the answer?????
------------------------------------------------------------------------------------------------
If iam WRONG please correct me, if i am correct and cleared your doubt Thank me

Sorry ia m not clear if the "10B" is also a number or its 10 times B.....
beyondenim plz tell the answer...Thanks.....

nandy1984 wrote: Lets say A = xy ( a two digit number ) = 10x+y
Then B = yx = 10y+x
Now the given equation is Q = 10B - A
= 100+B-A
=100 + 10y + x - 10x - y
= 100 + 9 (y - x)

I think you have messed up your calculation here
B by itself is a 2 digit integer. So say 13, would be 10(13) = 130

So we can find the value of Q only if u have the value of both x and y which are the tens digit of A ( ie x) and the tens digit of B ( ie y)
So answer is C

I think we cannot write 10B = 10 * B ....
Ex: 103 = 10 * 3 ????????
Hope i am clear..........
By the way whats the answer?????
------------------------------------------------------------------------------------------------
If iam WRONG please correct me, if i am correct and cleared your doubt Thank me

shankar.ashwin wrote:

nandy1984 wrote: Lets say A = xy ( a two digit number ) = 10x+y
Then B = yx = 10y+x
Now the given equation is Q = 10B - A
= 100+B-A
=100 + 10y + x - 10x - y
= 100 + 9 (y - x)

I think you have messed up your calculation here
B by itself is a 2 digit integer. So say 13, would be 10(13) = 130

So we can find the value of Q only if u have the value of both x and y which are the tens digit of A ( ie x) and the tens digit of B ( ie y)
So answer is C

I think we cannot write 10B = 10 * B ....
Ex: 103 = 10 * 3 ????????
Hope i am clear..........
By the way whats the answer?????
------------------------------------------------------------------------------------------------
If iam WRONG please correct me, if i am correct and cleared your doubt Thank me

i am not sure...i still have some doubt...Lets take B=43 and the above expression is Q = 10B - A so Q = 1043 - A ----> Q = 1000 + 43 - A....Is it not correct???? U might also be correct...Dont know...i think the person who has posted it better respond with the answer...Thanks....

Let us represent the 2 digit numbers as,
A=10x+y
B=10y+x
Q=10(10y+x)-10x-y = 99y. So we can rephrase the question as, what is the value of y?

Statement 1
x=7. Insufficient
Statement 2
y=6. Sufficient

Well the answer is B.

But I still don't get it! Let's try picking numbers method.

Q = 10b - a

Find: Q.

How can we find Q if we don't know the A AND B value?

Statement 1 - the tens digit of A is 7. Probably means the ones digit of B is 7. INS.

Statement 2 - the tens digit of B is 6. Probably means the ones digit of A is 6. INS.

But if we combine we immediately know that A is 76 and B is 67. SUF. My answer is C. But the book says otherwise...


HELP!

The trick is here is that they actually do not ask you to find either of the two numbers. If you are trying to find the two digit number A (or) B for that matter, you would obviously need both the statements together.

As posted in my solution earlier, we are asked to find 10B-A which is 99Y.

And to make it clear, we still do not know any of the numbers, but we can still find 'Q' which is 99(6)=594.

The number (A) can be anything here, say 66,76,56,16. For each of the numbers 10B-A is going to be the same - 99(6)=594

I hope this makes sense.

Say A = 10x+y, then B = 10y+x

Q = 10B-A = 10(10y+x)-(10x+y) = 99y

(1) The tens digit of A is 7.
Implies x = 7 Insufficient

(2) The tens digit of B is 6.
Implies y = 6 Sufficient

Answer B

Notes:
If number A is a two-digit positive integer and number B is a two-digit positive integer formed by reversing the digits of A, then

Sum of A and B is always divisible by 11
Difference of A and B is always divisible by 9

beyondenim wrote:Data Sufficiency: 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.

FIXED IT. SORRY ABOUT THAT

When a problem asks for the value of a STRANGE EXPRESSION -- in this case, 10B-A -- be suspicious: quite often there will be insufficient information to determine the values of the individual variables but SUFFICIENT information to determine the value of the STRANGE EXPRESSION.

Letting T = the tens digit and U = the units digit, we can represent any 2-digit integer as 10T+U.

Let A = 10T+U.
Since B reverses the digits:
B = 10U+T.

Q = 10B-A = 10(10U+T)-(10T+U) = (100U+10T) - 10T - U = 99U.

Question rephrased: What is the value of U?

Statement 1: The tens digit of A is 7.
Thus in A, 10T = 10*7, so T=7.
INSUFFICIENT.

Statement 2: The tens digit of B is 6.
Thus in B, 10U = 10*6, so U=6.
SUFFICIENT.

The correct answer is B.

I just came across this question so adding my 2c

Statement 1
A = 71 B = 17 Q = 170-71 = 99
A = 72 B = 27 Q = 270-72 = 198

Not Sufficient

Statement 2
A = 26 B = 62 Q = 620 - 26 = 594
A = 36 B = 63 Q = 630 - 36 = 594

Sufficient

Answer B