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Is w an integer?

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Math Expert
Joined: 02 Sep 2009
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19 May 2016, 03:30
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7
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Difficulty:

55% (hard)

Question Stats:

56% (01:20) correct 44% (01:08) wrong based on 153 sessions

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Is w an integer?

(1) 3w is an odd number.
(2) 2w is an even number.

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Re: Is w an integer?  [#permalink]

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19 May 2016, 03:45
1
Bunuel wrote:
Is w an integer?

(1) 3w is an odd number.
(2) 2w is an even number.

hi,
an excellent question, which requires that the info be extracted correctly from the available data..

(1) 3w is an odd number.
w can be a fraction or an integer..
a) w is an integer- w can take any ODD value....
b) w is a fraction - w can be any ODD/3 example

1/3 :- 3w = 3*1/3 =1........ 5/3 :- 3w = 5/3 * 3 = 5
so Insuff

(2) 2w is an even number.
Only possiblity is if w is an integer...
check for values-
2w = 6.... w=3......
2w=0...........w=0.....
2w=16.........w=8
ans is YES
Suff

B
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Re: Is w an integer?  [#permalink]

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19 May 2016, 16:56
2
1
Definitely B.

Stat. 1) 3w is an odd number
w = 1
3x1 = 3 --> odd
w = 1/3
3 x (1/3) = 1 --> odd & non-integer

Thus insufficient

Stat. 2) 2w is an even number.
w = 0
2 x 0 = even & int
w = 1
2 x 1 = even & int
we cannot use fractions for w for stat 2, because then we will not get even number, ex 2 x (1/2) = 1--> odd

Thus, we can say that w is an integer
Suff.

Ans: B
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Re: Is w an integer?  [#permalink]

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21 May 2016, 11:05
i took 2 * 1.7 =3.4 and concluded 'Not suff'.
This wrong ... why???
A fraction cannot be an even number....
Why???
Because....you can always append a zero to the end of the decimal representation without changing the value and ....

This is an explanation to all those who may get this qxn wrong because they overlooked this point or didnt know this(like me )
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21 May 2016, 12:03
1
Bunuel wrote:
Is w an integer?

(1) 3w is an odd number.
(2) 2w is an even number.

(1) 3w is an odd number.

So, 3w can be { 1, 3, 5 , 7 , 9 ........... }

If $$3w$$ = $$1$$ ;$$w$$ = $$\frac{1}{3}$$ ( NOT INTEGER)

If $$3w$$ = $$3$$ ;$$w$$ = $$1$$ ( INTEGER )

If $$3w$$ = $$5$$ ;$$w$$ = $$\frac{5}{3}$$ ( NOT INTEGER)

If $$3w$$ = $$7$$ ;$$w$$ = $$\frac{7}{3}$$ ( NOT INTEGER)

If $$3w$$ = $$9$$ ;$$w$$ = $$3$$( INTEGER)

(2) 2w is an even number.

So, 2w can be { 2, 4 , 6 , 8 , 10 ........... }

If $$2w$$ = $$2$$ ; $$w$$ = $$1$$ ( INTEGER)

If $$2w$$ = $$4$$ ; $$w$$ = $$2$$ ( INTEGER)

If $$2w$$ = $$6$$ ; $$w$$ = $$3$$ ( INTEGER)

If $$2w$$ = $$8$$ ; $$w$$ = $$4$$ ( INTEGER)

If $$2w$$ = $$10$$ ; $$w$$ = $$5$$ ( INTEGER)

Thus in all the cases you find that statement 2 is sufficient to answer the Question

nikhiljd

Plz go through this -

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Re: Is w an integer?  [#permalink]

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21 May 2016, 12:14
Definitely B.

the explanations given earlier are correct
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Re: Is w an integer?  [#permalink]

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22 May 2016, 03:45
Is w an integer?

(1) 3w is an odd number --> 3w = odd --> w = odd/3. Now, odd/3 can be an integer (for example if odd=3) as well as non-integer (for example if odd=5).Not sufficient.

(2) 2w is an even number --> 2w = even = 2k, where k is an integer --> w = even/2 = k = integer. Sufficient.

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Re: Is w an integer?  [#permalink]

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22 May 2016, 12:54
Bunuel wrote:
Is w an integer?

(1) 3w is an odd number.
(2) 2w is an even number.

(1) 3w is an odd number.

3w yields an odd integer.

w can be any odd integer or it can be 1/3.

Not sufficient.

2) 2w is an even number

To yield an even number w can take any integer value but not fraction.

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Re: Is w an integer?  [#permalink]

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07 Jun 2019, 21:10
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Re: Is w an integer?   [#permalink] 07 Jun 2019, 21:10
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