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If the smaller of two consecutive even integers is a multiple of 7, which of the following could NOT be the sum of these two integers?

Explanation	Calculations	Help
$We translate "two consecutive even integers" by letting the smaller be a and the next be a + 2 .$	$a, a + 2$	Theory & Tactics Method Card TRANS5-A Click to view full details
$We translate "the smaller is a multiple of 7" by writing a = 7 n, where n is an integer.$	$a = 7 n$	Theory & Tactics Method Card TRANS5-E Click to view full details
$Since a must be even, 7 n is even, so n must be even; we translate " n is even" by letting n = 2 m .$	$n = 2 m$	Theory & Tactics Method Card TRANS5-A Click to view full details
$We translate "the sum of these two integers" by forming a + (a + 2) .$	$Sum = a + (a + 2)$
$We substitute a = 7 n = 14 m into the sum and simplify.$	$14 m + (14 m + 2) = 28 m + 2$
$A valid sum must be of the form 28 m + 2 . Testing option E: 99 does not fit this form.$	$99 - 2 = 97 97 is not divisible by 28 99$

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E

If the smaller of two consecutive even integers is a multiple of 7, which of the following could NOT be the sum of these two integers?

Explanation	Calculations	Help
$We translate "two consecutive even integers" by letting the smaller be a and the next be a + 2 .$	$a, a + 2$	Theory & Tactics Method Card TRANS5-A Click to view full details
$We translate "the smaller is a multiple of 7" by writing a = 7 n, where n is an integer.$	$a = 7 n$	Theory & Tactics Method Card TRANS5-E Click to view full details
$Since a must be even, 7 n is even, so n must be even; we translate " n is even" by letting n = 2 m .$	$n = 2 m$	Theory & Tactics Method Card TRANS5-A Click to view full details
$We translate "the sum of these two integers" by forming a + (a + 2) .$	$Sum = a + (a + 2)$
$We substitute a = 7 n = 14 m into the sum and simplify.$	$14 m + (14 m + 2) = 28 m + 2$
$A valid sum must be of the form 28 m + 2 . Testing option E: 99 does not fit this form.$	$99 - 2 = 97 97 is not divisible by 28 99$

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E