If x is an integer, is (54 + 27)/x an integer ?

Question

(1) 6 <= x <= 81
(2) x is a multiple of 3

dollytaneja51 · Answer

Why C is not the correct answer?

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PKN · Answer

Hi  dollytaneja51 
Combined,

a) When x=9( multiple of 3 and  6\leq{x\leq{81}} ),  \frac{81}{x}=\frac{81}{9} =An INTEGER
b) When x=6( multiple of 3 and  6\leq{x\leq{81}} ),  \frac{81}{x}=\frac{81}{6} =NOT An INTEGER

Hence, E

Md231 · Answer

Alone, either is obviously not sufficient.

Together, 81/x wI'll be integer for 3, 9, 27 and not integers other values such as 6, 12, 18...

E.

monk123 · Answer

If x is an integer, is (54+27)/x an integer
Statement 1: 6 <= x <= 81
Statement 2: x is a multiple of 3

SOLUTION:

(54+27)/x = 81/x (for being an integer 81 should be wholly divided by x)

STATEMENT 1- 
if, x= 9, yes
if, x= 12, no

BCE

STATEMENT 2 - 
if, x=9, yes
if, x=12, no

now CE 
if,x= 9, yes
if,x=12, no

ANSWER (E)

sghosh1096 · Answer

We need to check if (54+27)/x (or 81/x or (3^4)/x ) is an integer or not.
if we combine the 2 statements, we get conditions 6<=x<=81 and x must be a multiple of 3.

if we take for example x=9, then the expression to check 81/x is an integer, but if we take say 18 or 36 (satisfies both the conditions provided in the statements) 81/x is not an integer. So we cannot be certain from the statements provided. Hence E

If x is an integer, is (54 + 27)/x an integer ?

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If x is an integer, is (54 + 27)/x an integer ?

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