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The integers a, b, c, d, and e are all positive. If a > d, c > b, e >

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The integers a, b, c, d, and e are all positive. If a > d, c > b, e > [#permalink]

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New post 06 Apr 2018, 05:04
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A
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E

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Question Stats:

85% (00:42) correct 15% (00:51) wrong based on 61 sessions

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The integers a, b, c, d, and e are all positive. If a > d, c > b, e > a, and b > e, what is the range of the five integers?

A. a - e
B. d - b
C. c - a
D. b - e
E. c - d

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The integers a, b, c, d, and e are all positive. If a > d, c > b, e > [#permalink]

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New post 06 Apr 2018, 20:27
Bunuel wrote:
The integers a, b, c, d, and e are all positive. If a > d, c > b, e > a, and b > e, what is the range of the five integers?

A. a - e
B. d - b
C. c - a
D. b - e
E. c - d

Write vertically, find greatest and smallest
This way is really easy

a > d
c > b
e > a
b > e

Look for one variable on RHS only.

It is NOT on LHS, thus NOT greater than any other.
It is the smallest.

d is on RHS only
Nothing is smaller than d
d is the smallest

Reverse the process.
Look for one variable on LHS only.

It is NOT on RHS, thus NOT smaller than any other.
It is the greatest.

c is on LHS only
Nothing is greater than c
c is the greatest

There is the range: (greatest - smallest) = (c - d)

Answer E

Reason through all values

1) a > d

2) c > b

3) e > a

4) b > e

****
1) a > d ____ ? Not much to work with

2) c > b, and b > e (#4).
So c > b > e

3) e > a
From #2 result, e is at the end
Now a is on the end
So c > b > e > a

4) b > e. Yeah, we knew that.

Only #1 is not accounted for, a > d

From results of #3: c > b > e > a
-- a > d
-- So c > b > e > a > d

Range:(greatest - smallest) = (c - d)

Answer E
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Re: The integers a, b, c, d, and e are all positive. If a > d, c > b, e > [#permalink]

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New post 06 Apr 2018, 20:44
1
Try to mark the numbers on the numberline for better visualization.

See the sketch .
Attachments

IMG_20180407_091404.jpg
IMG_20180407_091404.jpg [ 59.31 KiB | Viewed 588 times ]


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Re: The integers a, b, c, d, and e are all positive. If a > d, c > b, e > [#permalink]

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New post 08 Apr 2018, 16:42
start with d and a relation on a number line. e,b,c goes right to a in that order.

range = rightmost - leftmost = c-d

answer E
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Re: The integers a, b, c, d, and e are all positive. If a > d, c > b, e > [#permalink]

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New post 08 Apr 2018, 21:29
So basically I did this:

A > a
a < A
Then...
e > a, b > e, and c > b
So.... c > all a, e, b then c must be the biggest. and if a > d but a < e then d must be the smallest.
E


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Re: The integers a, b, c, d, and e are all positive. If a > d, c > b, e >   [#permalink] 08 Apr 2018, 21:29
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