Which of the following option represents all the possible values of \

Question

Which of the following option represents all the possible values of  ﻿\frac{ab}{c}  if  -3 < a < 5 ,  -6 < b < 3 , and  -4 < c < 6  and  ab
eq{0}  and c is a non zero integer?

A) ﻿ \frac{-30}{6} < \frac{ab}{c} < \frac{15}{6}

B)  \frac{-18}{6} < \frac{ab}{c} < \frac{15}{6}

C)  -18 < \frac{ab}{c} < 18

D)  -30 < \frac{ab}{c} < 30

E)  -30 < \frac{ab}{c} < 60  
 ﻿

chetan2u · Accepted Answer

The question is wrong the way it is written, as the range for integer values of a, b and c will be  -20\leq{\frac{ab}{c}}\leq{20} .
So, the question should not say a, b and c are integers.

-3 < a < 5 ,
  -6 < b < 3 , and 
 -4 < c < 6

﻿\frac{ab}{c}

MAX value....
c has to be of minimum numeric value, so |c|=1, and
a*b has to be maximum, |ab|<|5*-6|
so a~5, b~-6, and c=-1
 ﻿\frac{ab}{c}  ~ ﻿\frac{5*-6}{-1}  ......
 ﻿\frac{ab}{c}<\frac{-30}{-1}=30

MIN value....
c has to be of minimum numeric value, so |c|=1, and
a*b has to be maximum, |ab|<|5*-6|, but ab/c should be negative.
so a~5, b~-6, and c=1
 ﻿\frac{ab}{c}  ~ ﻿\frac{5*-6}{1}  ......
 ﻿\frac{ab}{c}>\frac{-30}{1}=-30

Range  -30<\frac{ab}{c}<30

D

https://www.youtube.com/watch?v=3nxR5EE0P-8

gorbyrodo · Answer

Im sorry but doesnt A has to be smaller than 5?  −3<a<5 
and B has to be bigger than -6?  −6<b<3

So D cannot be the answer here...

chetan2u · Answer

Hi, 
you are looking for the Range

Now max value of |ab| will be when absolute values of a and b are maximum, so |ab|=|4.99999...*-5.9999999..|, which is just less than |5*-6|.
That is why we are not taking it as  -30\leq{\frac{ab}{c}}\leq{30} , but  -30<{\frac{ab}{c}}<{30} , that is we are excluding the value |5*-6|

firas92 · Answer

Hi  chetan2u

Can we not consider 0<|c|<1?

Posted from my mobile device

chetan2u · Answer

Yes, we can consider c as a decimal, but then the range will go to infinity on both the sides, and that is why I have edited the question to read a and b as any values within the range and c as an integer. 
Thanks, I have edited the question accordingly.

JeffTargetTestPrep · Answer

Since -3 < a < 5 and -6 < b < 3, we have to consider the following products to make an inference about ab: (-3)(-6) = 18 (-3)(3) = -9 (5)(-6) = -30 (5)(3) = 15 -30 is the minimum, and 18 is the maximum, so we have: -30 < ab < 18 The interval for ab/c is the widest if the absolute value of c is the smallest. Since c is an integer in the interval -4 < c < 6, we have to consider two cases. If c = 1: -30 < ab/c < 18 If c = -1: 30 > ab/c > -18 Since both of the above intervals represent possible valid cases for ab/c, we can combine them into: -30 < ab/c < 30 Answer: D

kayarat600 · Answer

Why did we pick minus 1 and one for c instead of all ranges.

Krunaal · Answer

We wanted to find the maximum and minimum or the extremes, and to do so since  c  is in the denominator, if we keep its value 1 / -1 we can get the extremes; any other value from the range will be in-between those extremes.

Kinshook · Answer

Which of the following option represents all the possible values of  ﻿\frac{ab}{c}  if  -3 < a < 5 ,  -6 < b < 3 , and  -4 < c < 6  and  ab
eq{0}  and c is a non zero integer?

Minimum value of ab/c = (-30)/(1) = -30
Maximum value of ab/c = (-30)/(-1) = 30

-30 < ab/c < 30

IMO D

Which of the following option represents all the possible values of \

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Which of the following option represents all the possible values of ﻿\

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Which of the following option represents all the possible values of \