## Number problem

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### Number problem

by gmattaker2009 » Mon May 11, 2009 8:58 am
a two digit number is obtained either by multiplying the sum of the digits by 8 and subtracting 2 or by multiplying the difference of the digits by 15 and adding 2. find the number

ans is 62 . do let me know how you solve this problem

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by anksgupta » Mon May 11, 2009 11:03 am
Let tens digit be x and one's digit be y.
So number = 10x+y

Acc to ques.. 8(x+y)-2 = 10x+y....1)
15(x-y)+2=10x+y....2)

solving these 2 equations, You can get the required no as 62

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### Re: Number problem

by marcusking » Mon May 11, 2009 11:05 am
gmattaker2009 wrote:a two digit number is obtained either by multiplying the sum of the digits by 8 and subtracting 2 or by multiplying the difference of the digits by 15 and adding 2. find the number

ans is 62 . do let me know how you solve this problem
Lets start by taking the 2 digit multiples of 8 and subtracting 2 from them
14, 22, 30, 38, 46, 54, 62, 70, 78, 78, 86, 94

Now lets find the 2 digit multiples of 15 and add 2 to them
17, 32, 47, 62, 77, 92

Notice both sets have the number 62.

What does this tell us we know from the first set to get the 62 we had to multiply 8 by 8 and the problem tells us that the sum of the two digits multiplied by 8 would give us our number.
We are looking for 2 numbers that when added together give us 8

Also we know that we are looking for a 2 digit number that when it's digits are subtracted give us 4 (because (4 * 15) + 2 give us 62.

oddly enough 62 when it's digits are added together give us 8 and when subtracted give us 4 which fit both situations.

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