If x and y are integers, is y divisible by 3?

Question

(1) y = x^2 + x + 2
(2) y = 3x + 2

GMATinsight · Answer

Question: Is y divisible by 3?

An Insight: A number is divisible by 3 if sum of the digits is divisible by 3

Statement 1: y = x^2+x+2
@x=1, y= 4 so not divisible by 3
@x=2, y= 8 so not divisible by 3
@x=3, y= 14 so not divisible by 3
@x=4, y= 22 so not divisible by 3

Hence y is never divisible by 3
Sufficient

Statement 2: y=3x+2
I.e. y when divided by 3 will always leave remainder 2 as 3x is always divisible 3
Hence
Sufficient

Answer Option D

deveshmsn · Answer

statement 1 : y=x^2 + x + 2
x=1 y=4
x=2 y=8
x=3 y=14 Hence, y is not divisible by 3. UNIQUE ANSWER = SUFF

Statement 2: y=3x+2
x=1 y=5
x=2 y=8
x=5 y=17 Hence, y is not divisible by 3. UNIQUE ANSWER = SUFF

ANSWER=D

gmathopeful19 · Answer

D.

1) I didn't know how to do this any other way but test numbers:

X=2, y=8
X =3, y = 14
X = 5, y = 32

Clearly not divisible by 3

2) y = 3x + 2

y-2/(3) = x or y/3 = x + 2

See the trick? It's a remainder set up.

This means that y has a remainder of 2 when dividing by 3. Sufficient

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arvind910619 · Answer

Imo D 
Taking 1 0 and -1 we can see that none of the expression is divisible by 3 .

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KSBGC · Answer

Statement 1: y = x^2 + x + 2.

Now , x^2 + x = even ( all time ) regardless of the value of x .

even + 2 = even .

So, statement 1 is not divisible by 3.

Sufficient.

Statement 2: y = 3x + 2 .

Here 3x is divisible by 3 but 2 becomes remainder .

Thus , y is not divisible by 3.

Sufficient.

D is the correct answer.

Mallard · Answer

Bunuel  - Can you please explain how equation 1 is sufficient?

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

x and y are integers.
We have to find out if y is divisible by 3.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  y =  x^2  + x + 2

The expression on the RHS can be rewritten as x(x + 1) + 2.
Therefore, y = x(x + 1) + 2.

If x = 1, y = 1 (2) + 2 = 4. Is y divisible by 3? NO

If x = -1, y = -1 (0) + 2 = 2. Is y divisible by 3? NO

If x = 2, y = 2(3) + 2 = 8. Is y divisible by 3? NO

If x = 3, y = 3 (4) + 2 = 14. Is y divisible by 3? NO

So, we see that, regardless of whether x is a multiple of 3 or not, y is NEVER divisible by 3.

The data in statement 1 is sufficient to answer the question with a definite NO.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2:  y = 3x + 2

This tells us that y will always leave a remainder of 2, when divided by 3. Therefore, y is NEVER divisible by 3.

The data in statement 2 is sufficient to answer the question with a definite NO.
Statement 2 alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

hassi01 · Answer

In statement 1-
Even numbers can be divisible by 3,

3x2 = 6
3x4 = 12
3x6 = 18

and so on..

so y can be even and yet divisible by 3

If x and y are integers, is y divisible by 3?

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If x and y are integers, is y divisible by 3?

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