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19 Feb 2025, 01:30
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B
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Difficulty:
95%
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Question Stats:
30% (02:30) correct
70%
(02:31)
wrong
based on 107
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If 14x + 7y is divisible by all integers from 11 to 15, where x and y are integers, then which of the following statements must be true?
1. x - y is even
2. y^x is divisible by 2
3. xy is even
A. 2 only
B. 3 only
C. 1 and 3 only
D. 2 and 3 only
E. 1, 2, and 3
1. x - y is even
2. y^x is divisible by 2
3. xy is even
A. 2 only
B. 3 only
C. 1 and 3 only
D. 2 and 3 only
E. 1, 2, and 3
19 Feb 2025, 02:16
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We have 14x+ 7 = 7(2x+y), is divisible by integers 11 to 15
This means 7 (2x+y) is even, y is even. Which makes the following always true
3. xy is even = x*even = even
Eliminate A
For the other statements, we need to know the value of x to confirm others
Given 7(2x+y), is divisible by integers 11 to 15
7(2x+y) = LCM (11,12,13,14,15) * k (to account for higher multiples)
2x + y = 11* 4*3*13*5*k
2x = (even with 4) - y
x = (even) - y/2
We know y is even but we don't know if it is a multiple of 4
So
if y = 0, x is even
if y = 2n , where n is odd integer, x is odd
if y = 2n , where n is even integer, x is even
So x - y = even cannot be true always eliminate C,E
y^x, where x can be any integer even 0 or negative, that means y^x = even cannot be true always eliminate A and D
Answer B
This means 7 (2x+y) is even, y is even. Which makes the following always true
3. xy is even = x*even = even
Eliminate A
For the other statements, we need to know the value of x to confirm others
Given 7(2x+y), is divisible by integers 11 to 15
7(2x+y) = LCM (11,12,13,14,15) * k (to account for higher multiples)
2x + y = 11* 4*3*13*5*k
2x = (even with 4) - y
x = (even) - y/2
We know y is even but we don't know if it is a multiple of 4
So
if y = 0, x is even
if y = 2n , where n is odd integer, x is odd
if y = 2n , where n is even integer, x is even
So x - y = even cannot be true always eliminate C,E
y^x, where x can be any integer even 0 or negative, that means y^x = even cannot be true always eliminate A and D
Answer B
Bunuel
