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13 Feb 2023, 13:52
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E
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Difficulty:
95%
(hard)
Question Stats:
28% (03:12) correct
72%
(02:21)
wrong
based on 39
sessions
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If x and y are positive integers, is the sum of x and y a multiple of 2?
(l) The unit digit of \(128^x + 63^y\) is 9
(2) Unit digit of y is a prime factor of 14
(l) The unit digit of \(128^x + 63^y\) is 9
(2) Unit digit of y is a prime factor of 14
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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17 Feb 2023, 08:23
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If x and y are positive integers, is the sum of x and y a multiple of 2?
multiple of 2 implies is sum of x and y even integer.
(l) The unit digit of 128^x+63^y is 9
8 has cyclicity of 4 -
8^1 => 8
8^2 => 64
8^3 => 512
8^4 => 4096 and units digit repeats
3 has cyclicity of 4 -
3^1 => 3
3^2 => 9
3^3 => 27
3^4 => 81 and units digit repeats
for units digit to be 9, we have options (8 + 1) ; (2 + 7) ; (6 + 3)
i.e., x + y ::(1 + 4); (3 + 3) ; (4 + 1)
odd even odd
so x +y can be odd or even - statement 1 is not sufficient
(2) Unit digit of y is a prime factor of 14
prime factors of 14 are 2 and 7
But no information on x is given.
statement 2 is not sufficient.
statement 1 and 2 taken together.
if unit digit of y is 2 => one of the possible value of y s 12
and correspondingly x could be (1,5,9 etc)
sum of x and y is odd integer
if unit digit of y is 7 => one of the possible value of y is 7, 27 etc
and correspondingly x could be (3, 7, 11 etc)
sum of x and y is even integer.
therefore statement 1 and 2 taken together also is Not sufficient.
Answer E
multiple of 2 implies is sum of x and y even integer.
(l) The unit digit of 128^x+63^y is 9
8 has cyclicity of 4 -
8^1 => 8
8^2 => 64
8^3 => 512
8^4 => 4096 and units digit repeats
3 has cyclicity of 4 -
3^1 => 3
3^2 => 9
3^3 => 27
3^4 => 81 and units digit repeats
for units digit to be 9, we have options (8 + 1) ; (2 + 7) ; (6 + 3)
i.e., x + y ::(1 + 4); (3 + 3) ; (4 + 1)
odd even odd
so x +y can be odd or even - statement 1 is not sufficient
(2) Unit digit of y is a prime factor of 14
prime factors of 14 are 2 and 7
But no information on x is given.
statement 2 is not sufficient.
statement 1 and 2 taken together.
if unit digit of y is 2 => one of the possible value of y s 12
and correspondingly x could be (1,5,9 etc)
sum of x and y is odd integer
if unit digit of y is 7 => one of the possible value of y is 7, 27 etc
and correspondingly x could be (3, 7, 11 etc)
sum of x and y is even integer.
therefore statement 1 and 2 taken together also is Not sufficient.
Answer E
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