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# If a, b, c, and d are consecutive even integers and a < b < c < d, the

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Joined: 02 Sep 2009
Posts: 56304
If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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03 Jul 2018, 23:03
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If a, b, c, and d are consecutive even integers and a < b < c < d, then a + b is how much less than c + d ?

A. 2
B. 4
C. 6
D. 8
E. 10

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Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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03 Jul 2018, 23:13
(a+2 + a+3) - (a + a+1)
= 4 (B)
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Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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03 Jul 2018, 23:45
1
Bunuel wrote:
If a, b, c, and d are consecutive even integers and a < b < c < d, then a + b is how much less than c + d ?

A. 2
B. 4
C. 6
D. 8
E. 10

We can write the consecutive even integers in the form:
a=2n
b=2n+2
c=2n+4
d=2n+6 where n is a non-negative integer. $$n\geq{0}$$

Now a+b=4n+2 & c+d=4n+10

So, (c+d)-(a+b)=4n+10-(4n+2)=8

Ans. D
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Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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05 Jul 2018, 04:19
1

Solution

Given:
• a, b, c, and d are consecutive integers
• a < b < c < d

To find:
• Value of (c+d) – (a+b)

Approach and Working:
• The four positive integers (a, b, c and d) can be represented as 2n, 2n+2, 2n+4, 2n+6 respectively (since a<b<c<d), where n is an integer
• Value of (c+d) = (2n+4 + 2n+6) = 4n +10
• Value of (a+b) = (2n + 2n+2) = 4n + 2
• Thus, (c+d) –(a+b) = (4n+10) – (4n+2) = 8

Therefore, the value of (a+b) is 8 less than that of (c+d)

Hence, the correct answer is option D.

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If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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05 Jul 2018, 13:52
Bunuel wrote:
If a, b, c, and d are consecutive even integers and a < b < c < d, then a + b is how much less than c + d ?

A. 2
B. 4
C. 6
D. 8
E. 10

$$a, b, c, d$$
$$2, 4, 6, 8$$
$$(a+b)=(2+4)=6$$
$$(c+d)=(6+8)=14$$
$$(c+d)-(a+b)=(14-6)=8$$

The difference between and range of four consecutive integers will always be the same.

Test if in doubt with another number set:
$$6, 8, 10, 12$$
$$(22 - 14) = 8$$

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Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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09 Jul 2018, 19:57
Bunuel wrote:
If a, b, c, and d are consecutive even integers and a < b < c < d, then a + b is how much less than c + d ?

A. 2
B. 4
C. 6
D. 8
E. 10

We can let a, b, c, and d equal 2, 4, 6, and 8 respectively.

a + b = 2 + 4 = 6

c + d = 6 + 8 = 14

Thus, a + b is 14 - 6 = 8 less than c + d.

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Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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09 Jul 2018, 21:09
I use the substitution method in such a question:So use whatever consecutive even numbers that come to your mind.
For eg.2,4,6,8
By simple math in the mind,we get (6+8)-(2+4)=8,which is the answer.
I hope it helps
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Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the   [#permalink] 09 Jul 2018, 21:09
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