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two digit integers

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by rahul.s » Wed Feb 10, 2010 2:43 am
the number A is a 2 digit positive integer; the number B is the 2 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

OA is B
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Source: — Data Sufficiency |
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by papgust » Wed Feb 10, 2010 2:52 am
Let a and b be ten's digit and unit's digit respectively.

A = 10*a + b
B = 10*b + a [Reverse of A]

Q = 10B - A

Q = 10(10*b+a) - (10*a+b)

Q = 100b + 10a - 10a - b

Q = 99*b

Now we need to determine the value of 'b' or unit's digit.

A. a = 7.

We are only considered about b. Insufficient.

B. b = 6

YES. We can find the value of Q. Sufficient.
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by sanju09 » Thu Feb 11, 2010 4:02 am
rahul.s wrote:the number A is a 2 digit positive integer; the number B is the 2 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

OA is B
If A is 10 x + y then B is 10 y + x such that Q = 99 y or Q is 99 times the unit's digit of A or Q is 99 times the ten's digit of B. So, the question reduces to:

Either

What is the unit's digit of a 2 digit positive integer A?

Or

What is the ten's digit of a 2 digit positive integer B?


(1) This serves no purpose by itself. Insufficient

(2) This answers our main query straight away. Sufficient

[spoiler]B[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
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