If ab = c, is 72/b an integer? (1) c = 36 (2) 72/a is an integer

If ab=c, is \(\frac{72}{b}\) an integer?
This question actually asks whether b is a factor of 72.

(1) c=ab=36 --> \(b=\frac{36}{a}\)
If a =1/4, then \(b=\frac{36}{a}=144\). Consequently, \(\frac{72}{b}=\frac{1}{2}\) is NOT an integer.
If a =1, then \(b=\frac{36}{a}=36\). Consequently, \(\frac{72}{b}=2\) is an integer.
NOT SUFFICIENT

(2) \(\frac{72}{a}\) is an integer
Let's take c=36 for the sake of calculation
If a =1/4 and c=36, then \(\frac{72}{a}\) is an integer and \(b=144\). THUS, \(\frac{72}{b}=\frac{1}{2}\) is NOT an integer.
If a =1 and c=36, then \(\frac{72}{a}\) is an integer and \(b=36\). THUS, \(\frac{72}{b}=2\) is an integer.
NOT SUFFICIENT

(1)+(2)
c=ab=36 and 72/a is an integer.
If a =1/4, then \(\frac{72}{a}\) is an integer and \(b=144\). THUS, \(\frac{72}{b}=\frac{1}{2}\) is NOT an integer.
If a =1, then \(\frac{72}{a}\) is an integer and \(b=36\). THUS, \(\frac{72}{b}=2\) is an integer.
NOT SUFFICIENT

Final answer is (E)

(1) c=36 insufic

ab=36…(a,b)=anything

(2) 72/a is an integer insufic

\(a\) is a factor of 72, but we don't know if \(c\) is a factor of \((a,72)\)

(1&2) insufic

(a,b)=anything

Ans (E)

If ab = c, is \(\frac{72}{b}\) an integer?

Here a, b and c can be non integers or negative.

(1) c = 36
ab = 36
If b is a factor of 36 i.e. 1,2,3,4,5,9,12,18 and 36 then \(\frac{72}{b}\) is an integer.
If b is not a factor of 36 i.e. 2.1 where a is \(\frac{240}{7}\) then \(\frac{72}{b}\) is not an integer.

INSUFFICIENT.

(2) \(\frac{72}{a}\) is an integer
\(\frac{72}{a}\) = 72.\(\frac{b}{c}\)
Here if b and c are both multiple of 3 then \(\frac{72}{b}\) is an integer.
If b and c are multiple of 5 then \(\frac{72}{b}\) is not an integer.

INSUFFICIENT.

Together 1 and 2
\(\frac{72}{a}\) = 72.\(\frac{b}{36}\) = 2b
Since \(\frac{72}{a}\) is an integer b can be any integer
If b = 2 then \(\frac{72}{b}\) is an integer.
If b = 5 then \(\frac{72}{b}\) is not an integer.

INSUFFICIENT.

Answer E.

Given ab=c, we are to determine if 72/b is an integer.

It is worth noting that a,b, and c, are not restricted in the question and can, therefore, be any number.

Statement 1: c=36.
This implies ab=36.
This is not sufficient. a can be 3 and b will be 12. In this case, 72/12=6 which is an integer.
However when a=0.1, then b=360 in order to satisfy ab=36.
72/360 is not an integer. Hence statement 1 is not sufficient on its own.

Statement 2: 72/a is an integer.
Insufficient. This is because when a=1, 72/1 is an integer, but b does not necessarily have to be an integer. b can be 1.414 and 72/b will not be an integer. b can also be 2 and 72/b will be an integer. Statement 2 is hence not sufficient on its own.

1+2
Still not sufficient.
72/a is an integer, a =1 and a=0.1 satisfy this condition.
In addition, ab=36, when a=1, then b=36, implying 72/b is an integer. However, when a=0.1, then b=360 and 72/b is not an integer.
Statements 1 and 2 even when combined are not sufficient.

The answer is E.

(1) Factors of 36 are 1,3,4,6,12,18,36. All of them are also factors of 72. We need to express either a or b in a fractional term to examine whether 72/b results into an integer. Lets try, ab = 36, when a = 8, b = 9/2, then (72* 2/9) is an integer. a= 360, b = 1/10, then also 72/b is an integer. When a = 72, b = 17/28, then 72/ b = 72* 28/17, which is not an integer. Not sufficient.

(2) 72/ a = integer. no information about b. not sufficient.

(1) & (2) together,
in all the examples where b was fraction for statement (1), 72/a is an integer, but still when a = 72, b = 17/28, 72/b was not an integer. so, E is the answer imho.

If ab = c, is \(\frac{72}{b}\) an integer ?

(Statement1): c = 36
—> if ab= 18*2=36 —> \(\frac{72}{2}= 36\) (Yes)
—> if \(ab=( \frac{1}{4})*144= 36\) —> \(\frac{72}{144}= \frac{1}{2}\) (No)
Insufficient

(Statement2): \(\frac{72}{a}\) is an integer.
No info about what b is.
Clearly insufficient.

Taken together 1&2,

If a = 18, b= 2 —> ab=36, \(\frac{72}{a}\) — integer, then \(\frac{72}{b} = \frac{72}{2}= 36\) integer (yes)

If \(a= \frac{1}{4}\), b=144 —>\(( \frac{1}{4})*144=36\), \(\frac{72}{a}= \frac{72}{(1/4)}= 288\), then \(\frac{72}{ 144}= \frac{1}{2}\) (not integer —No)
Insufficient

The answer is E

Posted from my mobile device

This questions reinstates the Idea: Making undue assumptions on GMAT is suicide

Do not assume, a is integer.

E is the answer.