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If 0<b, and 0>ab, which of the following CANNOT be true?

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If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 15 Nov 2016, 09:49
1
3
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:34) correct 35% (01:47) wrong based on 171 sessions

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Re: If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 15 Nov 2016, 10:01
i think that it should be D.

SOLUTION:
b can be any positive no. as given that b>0
and
a is always negative as ab < 0

So take any value of a and b, say a = -2 and b = 1.
the a -1 is always negative & since b > 0 so answer can't be B and C as they will be always negative.

and for E , 1-a will be positive and you can take any higher value of a and lower value of b.

similarly A will always be positive. but when you put any value in D , you get you will always get negative value. since a- 1 will be always negative. so it can't be greater than 8.

so answer is D
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Re: If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 15 Nov 2016, 10:04
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Bunuel wrote:
If 0<b, and 0>ab, which of the following CANNOT be true?

A. (3b+5)/(1−a)>8
B. (a−1)/(3b+5)<8
C. (3b+5)/(a−1)<8
D. (3b+5)/(a−1)>8
E. (1−a)/(3b+5)>8



D

b>0 (b is positive) ab<0 (a is negative)

A. (3b+5)/(1−a)>8 positive/positive=positive can be true
B. (a−1)/(3b+5)<8 negative/positive=negative can be true
C. (3b+5)/(a−1)<8 positive/negative=negative can be true
D. (3b+5)/(a−1)>8 positive/negative= negative cannot be true
E. (1−a)/(3b+5)>8 positive/positive=positive can be true
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Re: If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 15 Nov 2016, 10:09
0<b implies b is positive
0>ab implies a is negative
A. (3b+5)/(1−a)>8 - Both numerator and denominator is positive, so possible

B. (a−1)/(3b+5)<8 - Numerator negative but denominator positive, so possible.

C. (3b+5)/(a−1)<8 - Numerator positive but denominator negative, so possible.

D. (3b+5)/(a−1)>8 - Numerator positive but denominator negative, so not possible to be >8.

E. (1−a)/(3b+5)>8 - Both numerator and denominator is positive, so possible

Hence answer is D.

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Re: If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 17 Nov 2016, 14:50
Bunuel wrote:
If 0<b, and 0>ab, which of the following CANNOT be true?

A. (3b+5)/(1−a)>8
B. (a−1)/(3b+5)<8
C. (3b+5)/(a−1)<8
D. (3b+5)/(a−1)>8
E. (1−a)/(3b+5)>8


Since 0 < b and 0 > ab, b must be positive and ab must be negative. If b is positive and ab is negative, then a must be negative. We need to determine which of the answer choices cannot be true.

Since each of the choices has at least one of the quantities 3b + 5, 1 - a, and a - 1, we can analyze whether those quantities are positive or negative.

Since b is positive, 3b + 5 is positive.

Since a is negative, 1 - a is positive.

Since a is negative, a - 1 is negative.

Now, let’s analyze each answer choice.

A) (3b+5)/(1−a) is the quotient between two positive quantities, so it must be positive and can be greater than 8.

B) (a−1)/(3b+5) is the quotient between a negative quantity and a positive quantity, so it must be negative and thus less than 8.

C) (3b+5)/(a−1) is the quotient between a positive quantity and a negative quantity, so it must be negative and thus less than 8.

D) By our analysis in answer choice C, we know that (3b+5)/(a−1) is negative; therefore (3b+5)/(a−1) is NOT greater than 8.

Answer: D
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Re: If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 18 Sep 2019, 08:38
Bunuel wrote:
If 0<b, and 0>ab, which of the following CANNOT be true?

A. (3b+5)/(1−a)>8
B. (a−1)/(3b+5)<8
C. (3b+5)/(a−1)<8
D. (3b+5)/(a−1)>8
E. (1−a)/(3b+5)>8



is the best approach for question is to attempt each option individually? or can we try any other approach
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Re: If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 23 Sep 2019, 09:35
Bunuel wrote:
If 0<b, and 0>ab, which of the following CANNOT be true?

A. (3b+5)/(1−a)>8
B. (a−1)/(3b+5)<8
C. (3b+5)/(a−1)<8
D. (3b+5)/(a−1)>8
E. (1−a)/(3b+5)>8


Since b is positive, a must be negative so that ab < 0.

Since (3b + 5) is positive, (1 - a) is positive, and (a - 1) is negative, the fractions in choices A, B, and E are positive and the fractions in choices C and D are negative. We see that D cannot be true.

Answer: D
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Re: If 0<b, and 0>ab, which of the following CANNOT be true?  [#permalink]

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New post 24 Sep 2019, 02:20
Actually, just by looking at the answer choices, we see that C and D are exactly the same just with reverse signs. Therefore, we could conclude that one of them must be incorrect.
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Re: If 0<b, and 0>ab, which of the following CANNOT be true?   [#permalink] 24 Sep 2019, 02:20
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