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If b<c<d and c>0, which of the following cannot be true if b,c and d

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If b<c<d and c>0, which of the following cannot be true if b,c and d  [#permalink]

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New post Updated on: 19 Jan 2017, 22:21
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If \(b < c < d\) and \(c > 0\), which of the following cannot be true if b, c and d are integers?

\(A. bcd > 0\)

\(B. b + cd < 0\)

\(C. b – cd > 0\)

\(D. \frac{b}{cd} < 0\)

\(E. b^{3} cd < 0\)

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Originally posted by hazelnut on 19 Jan 2017, 20:35.
Last edited by hazelnut on 19 Jan 2017, 22:21, edited 1 time in total.
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Re: If b<c<d and c>0, which of the following cannot be true if b,c and d  [#permalink]

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New post 19 Jan 2017, 21:10
b<c<d and c>0 => either b>0 or b<0

A.bcd>0. POSSIBLE if b>0

B.b+cd<0. POSSIBLE if b= -10, c=2, d=3

C.b–cd>0. NOT POSSIBLE.

D.bcd<0. POSSIBLE if b<0

E.(b^3)cd<0. POSSIBLE if b<0

Therefore, C.
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Re: If b<c<d and c>0, which of the following cannot be true if b,c and d  [#permalink]

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New post 19 Jan 2017, 22:20
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I have tested by using different sets of value to verify the result.


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Re: If b<c<d and c>0, which of the following cannot be true if b,c and d  [#permalink]

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New post 20 Jan 2017, 01:31
b< c < d && c> 0 ==> d>0 && (b<0 or b>0)

since c & d are greater than 0 ==> cd > 0 && cd > b
Thus, b - cd > 0 is not possible.

Ans.: C
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Re: If b<c<d and c>0, which of the following cannot be true if b,c and d  [#permalink]

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New post 03 Apr 2017, 11:04
b can be 0 as we are not given that b,c,d are positive integers.

Thus only choice C fits.
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Re: If b<c<d and c>0, which of the following cannot be true if b,c and d  [#permalink]

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New post 06 Apr 2017, 09:57
ziyuen wrote:
If \(b < c < d\) and \(c > 0\), which of the following cannot be true if b, c and d are integers?

\(A. bcd > 0\)

\(B. b + cd < 0\)

\(C. b – cd > 0\)

\(D. \frac{b}{cd} < 0\)

\(E. b^{3} cd < 0\)


We are given that b < c < d and c > 0, and that b, c, and d are integers.

Since c > 0, c is positive, and since d > c, d must also be positive. However, we are unsure of whether b is positive or negative. Let’s look at our answer choices to determine which MUST be true.

A. bcd > 0

If b is positive, then bcd is greater than zero. Answer choice A can be true.

B. b + cd < 0

If b is negative and its absolute value is greater than the product of cd, then b + cd is less than zero. For example, if b = -3, c = 1, and d = 2, we have -3 + (1)(2) = -1 < 0. Answer choice B can be true.

C. b - cd > 0

We can simplify answer choice C to read:

b > cd

If b is negative or zero, it certainly can’t be greater than cd, since cd is positive. If b is positive, it still can’t be greater than cd, since both c and d are integers greater than b. Thus, answer choice C can never be true.

Answer: C
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Re: If b<c<d and c>0, which of the following cannot be true if b,c and d  [#permalink]

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New post 18 Apr 2018, 17:56
This question can be done by this approach.
The key point is that b can be greater than , equal to or less than zero.
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Re: If b<c<d and c>0, which of the following cannot be true if b,c and d &nbs [#permalink] 18 Apr 2018, 17:56
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