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Math Expert V
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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Difficulty:   15% (low)

Question Stats: 74% (00:45) correct 26% (00:38) wrong based on 127 sessions

### HideShow timer Statistics 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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Manager  G
Joined: 14 Jun 2018
Posts: 222
Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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(a+2 + a+3) - (a + a+1)
= 4 (B)
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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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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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 2943
Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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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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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3090
If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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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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Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6967
Location: United States (CA)
Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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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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Manager  G
Status: In last prep stage
Joined: 11 Jun 2017
Posts: 155
GMAT 1: 630 Q44 V33 GMAT 2: 680 Q47 V37 GPA: 3.2
Re: If a, b, c, and d are consecutive even integers and a < b < c < d, the  [#permalink]

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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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Ankit
Target Score:730+

If the post was useful,please send the kudos 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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