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04 Nov 2010, 08:24
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C
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What is the sum of the digits of the positive integer n where n < 99?
(1) n is divisible by the square of the prime number y.
(2) y^4 is a two-digit odd integer.
(1) n is divisible by the square of the prime number y.
(2) y^4 is a two-digit odd integer.
04 Nov 2010, 09:20
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samark
What is the sum of the digits of the positive integer n where n < 99?
(1) n is divisible by the square of the prime number y --> clearly insufficient, as no info about y.
2) y^4 is a two-digit odd integer --> also insufficient, as no info about n, but from this statement we know that if y is an integer then y=3 (y must be odd in order y^4 to be odd and it cannot be less than 3 or more than 3 since 1^4 and 5^4 are not two digit numbers).
(1)+(2) Since from (1) y=integer then from (2) y=3, so n is divisible by 3^2=9. Number to be divisible by 9 sum of its digits must be multiple of 9, as n is two-digit number <99 then the sum of its digits must be 9 (18, 27, 36, ..., 90.). Suffiicient.
Answer: C.
General Discussion
26 Nov 2011, 06:09
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1. INSUFFICIENT
e.g. take y = 2,
if n = 6, 6 x 2^2 = 24, sum of digits is 6
if n = 3, 3 x 2^2 = 12, sum of digits is 3
2. INSUFFICIENT
e.g.
y = 3 then y^4 = 81 (a 2 digit odd number)
if y = 5^1/2 then y^4=25 (a 2 digit odd number)
1. & 2. SUFFICIENT y = 3 (the only prime number with an odd two digit result when raised to the 4th power)
therefore n is a multiple of 9, and the sum of the digits of all multiples of 9 is 9.
e.g. take y = 2,
if n = 6, 6 x 2^2 = 24, sum of digits is 6
if n = 3, 3 x 2^2 = 12, sum of digits is 3
2. INSUFFICIENT
e.g.
y = 3 then y^4 = 81 (a 2 digit odd number)
if y = 5^1/2 then y^4=25 (a 2 digit odd number)
1. & 2. SUFFICIENT y = 3 (the only prime number with an odd two digit result when raised to the 4th power)
therefore n is a multiple of 9, and the sum of the digits of all multiples of 9 is 9.
