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chetan2u
Is x an integer?
(1) 7x is an integer
(2) x \(\neq{\frac{1}{7}}\)

New question!!!..

Question stem:- Is x an integer?

St1:- 7x is an integer

Possibilities of x:- 'Integer(Such as -1,1,0 etc.), rational numbers(such as -1/7,1/7 etc or any number with 7 in denominator)
No unique value of x.
Insufficient.

St2:- x \(\neq{\frac{1}{7}}\)
Possibilities of x:- 'Integer(Such as -1,1,0 etc.), rational numbers(such as -1/2,1/2 etc except 1/7)
No unique value of x.
Insufficient.

Combined, x can be integers and fractions too.
Insufficient.

Ans. (E)
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chetan2u
Is x an integer?
(1) 7x is an integer
(2) x \(\neq{\frac{1}{7}}\)

New question!!!..
1=> x can be 2,3,4 etc meaning 7x is an integer so x is an integer
x can be 1/7, 2/7,3/7 etc meaning 7x is an integer so x is not an integer

1 is not sufficient

2 => x \(\neq{\frac{1}{7}}\) x can be 2,3,4 or 2/7,3/7 etc

2 is not sufficent

Both 1 and 2 are insufficient

Hence the Answer is E.
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chetan2u
Is x an integer?
(1) 7x is an integer
(2) x \(\neq{\frac{1}{7}}\)

New question!!!..

From 1:
X can be 1,2,3,4 or 1/7 or -(1/7)
Hence NS

From 2:
X is not 1/7 but X can be 1,2,3,-4,-5 or X can be -(1/7)
NS

1+2
NS

Ans: E
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