If a,b,c,d are integers such that both (-2a) * (−3c) * b and

Question

If a,b,c,d are integers such that both  (-2a) * (−3c) * b  and  d * (-2b) * 5a  are positive, which of the following expressions is always negative?

A) a*b
B) b*c
C) c*d
D) a*d
E) a*c

chetan2u · Accepted Answer

Hi,
good Q..

(-2A) * (−3C) * B  and  D * (-2B) * 5A  are positive
so their product should also be positive..
therefore  (-2A) * (−3C) * B * D * (-2B) * 5A  is positive..
0r  A^2*B^2*C*D*(-60)  IS POSITIVE..
so  C*D*(-60)  should be positive..
or C*D should be negative
C

ENGRTOMBA2018 · Answer

A question that makes you realize the pattern therein.

You are given that  (-2a) * (−3c) * b  > 0 ----> abc > 0 ....(1)

and  d * (-2b) * 5a  ----> abd < 0 ...(2)

From 1 and 2, 2 cases are possible

1. Case 1, a (+), b(+), c(+), d(-) ---> eliminate A,B and E.

2. Case 2, a (-), b(-), c(+), d(-) ---> eliminate D.

Thus C is the only remaining option and is hence the correct answer.

Hope this helps.

naumyuk · Answer

Don't pay attention to quotients. They don't have any influence.

To make the expressions easier for understanding rewrite them in the following way:

Expression abc = positive
Expression abd = negative

In order to be positive and negative correspondingly 'abc' and 'abd' components have to have following set of signs:
abc abd
+++ ++-
+-- +-+
-+- -++
--+ ---

So, we can see that for each pair c and d always have different signs. Therefore for all possible options c*d must be negative.

ajdse22 · Answer

Nice question
Since (-2a)*(-3c)*b> 0 => 6*a*b*c>0 = > a*b*c>0----1
d*(-2b)*(5a)>0 => -10*d*b*a>0- ==> d*b*a<0 ----2

Now let us look at the choices
A and B -- a*b and b*c . Well a*b can be positive in which case c>0 and a*b<0 in which case c<0 . The same thing applies to choice B and hence both are not correct choices
> 0
Let us look at D and E - a*d and a*c respectively. For reasons noted above if b<0 then a*c<0 but if b>0 then a*c >0. Also a*d for the same reason can be +ve and -ve.
Which brings us to C. At this stage we can check this answer and go.. But let us see what is going on

if c<0 then from inequality (1) a*b*c> 0 ==> that a*b <0 . From inequality (2) d*b*a<0 we see that if a*b<0 then d>0 ===> c*d<0
if c>0 then a*b>0 . From (2) d<0 ==> again c*d<0 so answer choice C!

KarishmaB · Answer

A simple analysis will help you.

The given expressions are (ignoring co-efficients):
abc is positive.
-abd is positive.

Note that both have ab common so whatever sign that brings, will be same in both products. If c and d had the same signs, abc and abd would have the same sign so abc and -abd would have opposite signs. 
So c and d must have opposite signs so that both abc and -abd have the same sign (positive).

Answer (C)

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If a,b,c,d are integers such that both (-2a) * (−3c) * b and

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If a,b,c,d are integers such that both (-2a) * (−3c) * b and

Prep Toolkit

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