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shameekv1989
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Which of the following option represents all the possible values of \ Updated on: 24 Apr 2020, 22:40
Originally posted by shameekv1989 on 22 Apr 2020, 16:12.
Last edited by chetan2u on 24 Apr 2020, 22:40, edited 2 times in total.
Corrected the Q
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56% (02:29) correct 44% (02:48) wrong based on 355 sessions

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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 \(ab\neq{0}\) 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) \(-30 < \frac{ab}{c} < 60 \)

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D
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chetan2u
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Which of the following option represents all the possible values of \ 22 Apr 2020, 22:18
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shameekv1989
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 a, b, and c are non-zero integers?

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) \(-30 < \frac{ab}{c} < 60 \)

Show more


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

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Which of the following option represents all the possible values of \ 24 Apr 2020, 11:29
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chetan2u
shameekv1989
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 a, b, and c are non-zero integers?

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) \(-30 < \frac{ab}{c} < 60 \)



\(-3 < a < 5\),
\( -6 < b < 3\), 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
Show more


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...
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Which of the following option represents all the possible values of \ 24 Apr 2020, 22:01
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gorbyrodo
chetan2u
shameekv1989
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 a, b, and c are non-zero integers?

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) \(-30 < \frac{ab}{c} < 60 \)



\(-3 < a < 5\),
\( -6 < b < 3\), 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


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...
Show more

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|
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Which of the following option represents all the possible values of \ 24 Apr 2020, 22:29
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chetan2u
shameekv1989
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 a, b, and c are non-zero integers?

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) \(-30 < \frac{ab}{c} < 60 \)



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

Show more

Hi chetan2u

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

Posted from my mobile device
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chetan2u
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Which of the following option represents all the possible values of \ 24 Apr 2020, 22:43
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chetan2u
shameekv1989
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 a, b, and c are non-zero integers?

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) \(-30 < \frac{ab}{c} < 60 \)



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


Hi chetan2u

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

Posted from my mobile device
Show more

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.
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Which of the following option represents all the possible values of \ 27 Jun 2023, 13:53
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shameekv1989
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 \(ab\neq{0}\) 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) \(-30 < \frac{ab}{c} < 60 \)
Show more

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
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Which of the following option represents all the possible values of \ 01 Apr 2025, 14:17
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Why did we pick minus 1 and one for c instead of all ranges.
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Which of the following option represents all the possible values of \ 01 Apr 2025, 15:00
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Why did we pick minus 1 and one for c instead of all ranges.
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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.
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Which of the following option represents all the possible values of \ 01 Apr 2025, 22:07
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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 \(ab\neq{0}\) 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
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