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Data Sufficiency: The number A is a two-digit positive

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Data Sufficiency: The number A is a two-digit positive

by beyondenim » Wed Oct 19, 2011 8:42 am
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
Last edited by beyondenim on Wed Oct 19, 2011 8:49 am, edited 1 time in total.
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by nandy1984 » Wed Oct 19, 2011 8:47 am
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?
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by shankar.ashwin » Wed Oct 19, 2011 8:50 am
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
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by nandy1984 » Wed Oct 19, 2011 8:55 am
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 :)
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by nandy1984 » Wed Oct 19, 2011 8:58 am
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.....
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by shankar.ashwin » Wed Oct 19, 2011 9:00 am
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 :)
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by nandy1984 » Wed Oct 19, 2011 9:16 am
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....
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by sl750 » Wed Oct 19, 2011 10:06 am
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
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by beyondenim » Thu Oct 20, 2011 12:33 am
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!
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by shankar.ashwin » Thu Oct 20, 2011 12:55 am
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.
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by neelgandham » Thu Oct 20, 2011 2:08 am
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
Anil Gandham
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by GMATGuruNY » Thu Oct 20, 2011 4:03 am
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.
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by melguy » Fri Nov 04, 2016 7:32 pm
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
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