xy and yx are reversed two digit integers. If the sum of the digits eq

Question

xy and yx are reversed two digit integers. If the sum of the digits equals the difference between the squares of the digits, what could be the product of the digits?

A. 8
B. 12
C. 15
D.18
E. 24

vinguyen1503 · Answer

Just calculate each option. For B 1+2=3 and 2^2-1=4-1=3.

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Lowkya · Answer

If the sum of the digits equals the difference between the squares of the digits.
=> (x + y) = (x^2 - y^2)
=> (x + y) = (x + y)(x - y)
=>x-y = 1
So, XY = 21, 32, 43, 54, 65, 76, 87, 98

From the above possible numbers, the only product in options is 12 for number 43.

Answer: B

Shef08 · Answer

Can u explain how did u arrive at B? It is asking product of the digits

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Lowkya · Answer

Sure.
Yes, it is asking for the product of digits.

From the above solution you can see that possible numbers are XY = 21, 32, 43, 54, 65, 76, 87, 98.
=> Possible products are - 2, 6, 12,20, 30, 42, 56, 72.

Only 12 is in the options. So, B.

Hope this helps.

Thanks

ScottTargetTestPrep · Answer

Without loss of generality of the problem, we can assume that x > y. So we have:

x + y = x^2 - y^2

x + y = (x + y)(x - y)

Dividing both sides of the equation by (x + y) (since it won’t be 0), we have:

1 = x - y

The only way we can get (x - y) to equal 1 is if x is one more than y. Therefore, we see that x and y must be consecutive integers. Of the answer choices, we see that only 12 can be the product of two consecutive integers (12 = 3 x 4), so 12 is the correct answer.

Answer: B

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xy and yx are reversed two digit integers. If the sum of the digits eq

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xy and yx are reversed two digit integers. If the sum of the digits eq

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