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

Question

Competition Mode Question

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

(1)  c = 36

(2)  \frac{72}{a}  is an integer

madgmat2019 · Answer

If ab=cab=c, is 72/b an integer?

(1) c=36.........then a,b can be or cannot be integers......so insufficient

(2) 72/a is an integer........a can be 72/73 which results in b= something which cannot make 72/b as integer.......INSUFFICIENT

combining both we get b=36*73/72.......then also its INSUFFICIENT

OA:E

Archit3110 · Answer

72 = 2^3*3^2
#1
c=36 ; 2^2*3^2
so b can be either of 2^2 or 3^2 , hence 72/b will be an integer
if b ,a either of them may be a fraction or integer insufficeint
#2
72/a is an integer , and a*b=c
yes , when a= 2 and b = any even digit , but no when a = 2 and b = 5,7 
Insufficient
combining , no info
IMO E
If ab=c, is 72/b an integer?

(1) c=36

(2) 72/a is an integer

freedom128 · Answer

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)

exc4libur · Answer

(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)

unraveled · Answer

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.

eakabuah · Answer

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.

minustark · Answer

(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.

lacktutor · Answer

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

hero_with_1000_faces · Answer

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

Do not assume,  a  is integer.

E is the answer.

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

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

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