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# The number A is a two-digit positive integer; the number B i

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Manager
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The number A is a two-digit positive integer; the number B [#permalink]  22 Jul 2011, 08:18
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:02) correct 39% (01:20) wrong based on 74 sessions
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 able to get the value of Q using (1) which is contrary to the provided answer.

(1)
A = 7/10 + x
B = x/10 + 7

Q=10B-A
Q=10(x/10 + 7) - (7/10 + x)
Q= x + 70 - 7/10 - x
Q= 10x + 700 - 7 - 10x
Q= 700 - 7
Q= 693

Does this mean that the answer provided by Manhattan is wrong?
[Reveal] Spoiler: OA

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Senior Manager
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Re: unknown digits [#permalink]  22 Jul 2011, 09:09
A=10x+y
B=10y+x
10B-A=10[10y+x]-10x-y=100y+10x-10x-y=99y

Stmt1: The tens digit of A is 7 i.e 10x=7. But we don't know Y. Insufficient.

Stmt2: The tens digit of B is 6 i.e 10y=6 y=0.6
Q=99y=99*0.6=59.4 Sufficient.

OA B
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The number A is a two-digit positive integer; the number B i [#permalink]  05 Dec 2011, 16:59
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.
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Posts: 4
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Re: DS Questions [#permalink]  06 Dec 2011, 09:20
Example 1: If A is 61 then B is 16

10 (61) - 16 = 594

Example 2: If A is 67 then B is 76

10 (67) - 76 =594

So it doesn't matter what the ones digit is; the answer is going to be 594 all the time..
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Re: DS Questions [#permalink]  06 Dec 2011, 09:22
If the equation was 10A - B, then A's tens digit would have been important.
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Re: DS Questions [#permalink]  06 Dec 2011, 10:30
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Let X be the tens digit, Y be the units digit .

so A=10(X)+Y, B=10(Y)+X.
Q=10(B)-(A)
10(10(Y)+X)-10(X)+Y.
100(Y)+10(X)-10(X)+Y
100(Y)+10(X)-10(X)+y
Q=100(Y)+Y.
we can rephrase the question as" what is units digit of A i.e Y?"

stmmnt(2) tells that that the Y is 6. So the answer is B
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Re: DS Questions [#permalink]  06 Dec 2011, 10:48
B is sufficient to answer this.
let A be 10y+x (x- units digit, y- tens digit)
so B = 10x+y since it is reverse of A
hence Q=10B-A becomes
Q=10 (10x+y) -(10y+x)
=100x + 10y - 10y -x
=99x
so we only need the units digit of A

Statement 1 gives us the 10s digit of A - Insufficient
Statement 2 gives us the 10s digit of B which is the units digit of A hence x=6 => sufficient

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The number A is a two-digit positive integer; the number B i [#permalink]  04 Nov 2014, 08:18
386390 wrote:
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 able to get the value of Q using (1) which is contrary to the provided answer.

(1)
A = 7/10 + x
B = x/10 + 7

Q=10B-A
Q=10(x/10 + 7) - (7/10 + x)
Q= x + 70 - 7/10 - x
Q= 10x + 700 - 7 - 10x
Q= 700 - 7
Q= 693

Does this mean that the answer provided by Manhattan is wrong?

Let A= 10x + y and B =10y + x
1)
it is stated that the tens digit is 7. so x=7 which makes A= 70 + y and B=10y +7
now on solving: Q= 10B-A= 10 (10y+7) - 70-y
Q=99y, we don't know value of y, so insuff.
2)
tens digit of b is 6.
A= 10x+6 and B = 60+x
putting values,
Q= 10 (60+x) - 10x-6
Q=594 so (2) is sufficient ALONE
The number A is a two-digit positive integer; the number B i   [#permalink] 04 Nov 2014, 08:18
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