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two two-digit numbers

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two two-digit numbers

by sanju09 » Tue Mar 16, 2010 5:08 am
P, Q, and R are three digits such that the difference between the highest and second highest two-digit numbers formed by using two of P, Q, and R is 5. Also, the smallest two two-digit numbers formed in the same way, differ by 2. If Q > P > R, then what is the value of Q?
(A) 1
(B) 5
(C) 6
(D) 7
(E) 8
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by kstv » Tue Mar 16, 2010 5:21 am
The number are Q>P>R
10Q+P - (10Q+R ) = 5 = P-R
10R+Q - (10R+P) = 2 = Q-R
Q-R = 7 Q has to 8
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by sanju09 » Tue Mar 16, 2010 5:26 am
kstv wrote:The number are Q>P>R
10Q+P - (10Q+R ) = 5 = P-R
10R+Q - (10R+P) = 2 = Q-R
Q-R = 7 Q has to 8
How do we decide that R cannot be zero?
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by kstv » Tue Mar 16, 2010 5:34 am
we are talking of 2 digit numbers
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by sanju09 » Tue Mar 16, 2010 5:37 am
kstv wrote:we are talking of 2 digit numbers
right
10R+Q - (10R+P) = 2 = Q-R
RIGHT
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by [email protected] » Tue Mar 16, 2010 9:58 pm
Since Q is the biggest number, the biggest 2 digit number that can be formed is QQ
Since R is the smallest number, the smallest 2 digit number that can be formed is RR

Therefore,

(10Q+Q) - (10Q+P) = 5
Q-P = 5

(10R+P) - (10R+R) = 2
P-R = 2

1 and 5 are ruled out. 6 cannot be the answer cos that will make P=1 and R = -3. 7 cannot be the answer cos it will make P=2 and R=0.
IMHO Answer is [spoiler](E)8[/spoiler]
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by GMATSUCKER » Wed Mar 17, 2010 1:56 am
Is this a real GMAT Question ?
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