avaneeshvyas wrote:
Please correct my approach if it is wrong
Let p be the greater number and of the form 10x+y
q be of the form 10y+x
Statement 1:
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p+q = 110
11(x+y) = 110
x+y = 10
Only two single digit prime numbers supporting this are 7 and 3. Hence sufficient
Statement 2:
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p - q = 36
9(x-y) = 36
x-y = 4
Only two single digit prime numbers supporting this are 7 and 3. Hence sufficient
Option D
I don't think 1 is a prime number, so I wonder why any of you shortlisted numbers with digits 1 in the run up to your solutions
Yes, 1 is NOT prime. The smallest prime is 2.
Also, we are told that p and q are primes. Now, the digits of p (or q) could be primes and p (or q) could be non-primes. For example, 25, 27, 32, ...
p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?Given: \(p=prime=10x+y\) and \(q=prime=10y+x\), for some non-zero digits \(x\) and \(y\) (any two digit number can be expressed as \(10x+y\) but as both \(p\) and \(q\) are
two-digit then \(x\) and \(y\) must both be non-zero digits).
(1) p + q = 110 --> \((10x+y)+(10y+x)=110\) --> \(x+y=10\). Now, if we were not told that \(p\) and \(q\) are primes than they could take many values: 91 and 19, 82 and 28, 73 and 37, 64 and 46, ... Thus the larger number could be: 91, 82, 73, or 64. But as we are told that both \(p\) and \(q\) are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.
(2) p – q = 36 --> \((10x+y)-(10y+x)=110\) --> \(x-y=4\). Again, if we were not told that \(p\) and \(q\) are primes than they could take many values: 95 and 59, 84 and 48, 73 and 37, 62 and 26, 51 and 15. Thus the larger number could be: 95, 84, 73, 62, or 51. But as we are told that both \(p\) and \(q\) are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.
Answer: D.
OPEN DISCUSSION OF THIS QUESTION IS HERE: p-and-q-are-different-two-digit-prime-numbers-with-the-same-98912.html