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AS #73

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AS #73

by oquiella » Sun Oct 25, 2015 3:29 pm
73. Find the two digit number.
(1) The number is 4 times the sum of its digits.
(2) The number is 5 times the sum of its digits.
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by theCEO » Sun Oct 25, 2015 4:13 pm
oquiella wrote:73. Find the two digit number.
(1) The number is 4 times the sum of its digits.
(2) The number is 5 times the sum of its digits.
Two digits number = XY = 10X + Y

(1) The number is 4 times the sum of its digits
10X + Y = 4(X+Y)
10X + Y = 4X + 4Y
6X = 3Y
2X = Y
One digit is 2 times the ten digit

Number could be 12,24,36 or 48

(2) The number is 5 times the sum of its digits
10X + Y = 5(X+Y)
10X + Y = 5X + 5Y
5X = 4Y
(5/4)X = Y
One digit is 5/4 times the 10 digit

Number = 45

option b
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by Matt@VeritasPrep » Sun Oct 25, 2015 10:28 pm
This is a broken question. If the sum of the digits = d, we have

4d = 5d,

or

d = 0

You can see from theCEO's answer above that the two statements HAVE NO COMMON SOLUTIONS.

This is a huge no-no on the GMAT, and I would advise against using any more problems from this source.
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