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# The integer a is less than −1, and the integer d is greater than 1. If

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Math Expert
Joined: 02 Sep 2009
Posts: 62282
The integer a is less than −1, and the integer d is greater than 1. If  [#permalink]

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18 Mar 2020, 07:34
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Difficulty:

95% (hard)

Question Stats:

28% (03:02) correct 72% (01:52) wrong based on 57 sessions

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The integer a is less than −1, and the integer d is greater than 1. If −1 < b < 0 and 0 < c < 1, then which of the following must be the greatest negative number?

A. b − a
B. b − c
C. b − d
D. c − a
E. a − c

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Manager
Joined: 30 Jun 2019
Posts: 136
Re: The integer a is less than −1, and the integer d is greater than 1. If  [#permalink]

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20 Mar 2020, 14:10
a<-1
d>1
-1<b<0
0<c<1

How are you to decide between option C and E?
C) b-d --> small negative - large positive = large negative (-0.5 - 5 = -5.5)
E) a-c --> large negative - small positive = large negative (-5 - 0.5 = -5.5)
Intern
Joined: 09 Dec 2019
Posts: 2
Re: The integer a is less than −1, and the integer d is greater than 1. If  [#permalink]

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23 Mar 2020, 08:23
Intern
Joined: 09 Apr 2016
Posts: 2
The integer a is less than −1, and the integer d is greater than 1. If  [#permalink]

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23 Mar 2020, 12:58
2
The clue: the greatest number is the smallest number without the negative sign.
Greatest negative number will be the closest number to integer 0.

On the number line a lies between (-infinity) and (-1).
D lies between (+1) and (+infinity).
B is placed between (-1) and 0.
C is placed between 0 and (+1).

Option A:b − a
b-a will result in a positive value since b will always be -ve and -(a) will be positive.

Option B:b − c
b-c will result in a negative number which is close to the number 0. The subtraction will not result in number 0 as b is negative and -c will also be negative. This is a possible candidate.

Option C:b − d
b-d will result in a negative number. This number is definitely smaller than -1. b is smaller than -1 and d is greater than +1.

Option D:c − a
c − a will result in a positive value.

Option E: a − c
a-c will also result in a large negative number, but it will be smaller than the number which will form by option B.

Hence, the answer should be B.
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Re: The integer a is less than −1, and the integer d is greater than 1. If  [#permalink]

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25 Mar 2020, 08:42
2
Bunuel wrote:
The integer a is less than −1, and the integer d is greater than 1. If −1 < b < 0 and 0 < c < 1, then which of the following must be the greatest negative number?

A. b − a
B. b − c
C. b − d
D. c − a
E. a − c

We can let a = -2, b = -0.5, c = 0.5 and d = 2. Thus we have:

A. b - a = -0.5 - (-2) = 1.5

B. b - c = -0.5 - 0.5 = -1

C. b - d = -0.5 - 2 = -2.5

D. c - a = 0.5 - (-2) = 2.5

E. a - c = -2 - 0.5 = -2.5

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Intern
Joined: 23 Mar 2020
Posts: 22
The integer a is less than −1, and the integer d is greater than 1. If  [#permalink]

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25 Mar 2020, 20:48
Bunuel wrote:
The integer a is less than −1, and the integer d is greater than 1. If −1 < b < 0 and 0 < c < 1, then which of the following must be the greatest negative number?

A. b − a
B. b − c
C. b − d
D. c − a
E. a − c

Since the question says that the correct answer must be the greatest negative number, you can use any test values that fall within the limits in the question.

Let a = -2, b = -(1/2), c = (1/2), and d = 2

A) 1.5
B) -1
C) -2.5
D) 2.5
E) -2.5

The greatest negative number is -1, so the answer is (B)
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Joined: 16 Oct 2010
Posts: 10219
Location: Pune, India
Re: The integer a is less than −1, and the integer d is greater than 1. If  [#permalink]

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25 Mar 2020, 23:23
2
Bunuel wrote:
The integer a is less than −1, and the integer d is greater than 1. If −1 < b < 0 and 0 < c < 1, then which of the following must be the greatest negative number?

A. b − a
B. b − c
C. b − d
D. c − a
E. a − c

'Greatest negative number' means 'negative number with the smallest absolute value'.

--------- (a) ---------- -1 ---- (b) ---- 0 ---- (c) --- 1 ---------- (d) ----------

A. b − a
Not negative
B. b − c
Negative value with small absolute value
C. b − d
Negative value with large absolute value
D. c − a
Not negative
E. a − c
Negative value with large absolute value

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Karishma
Veritas Prep GMAT Instructor

Re: The integer a is less than −1, and the integer d is greater than 1. If   [#permalink] 25 Mar 2020, 23:23
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