If y 0, is (y^3 – y) divisible by 4?

Question

If y > 0, is (y^3 – y) divisible by 4?

(1) y^2 + y is divisible by 10.
(2) For a certain integer k, y = 2k + 1.

Bunuel · Accepted Answer

If y>0, is y^3-y divisible by 4?

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

(1) y^2+y is divisible by 10 --> if  y=10  then  y(y-1)(y+1)=10*9*11 , so not divisible by 4 (product of 2 odd and not multiple of 4 will not be divisible by 4) BUT if  y=100  then  y(y-1)(y+1)=100*99*101 , so divisible by 4 (100 is a multiple of 4, hence product will be divisible by 4). Not sufficient.

(2) For a certain integer k, y=2k+1 -->  y=odd  -->  y-1=even  and  y+1=even  -->  y(y-1)(y+1)  is a multiple of 4 (product of 2 even numbers is a multiple of 4, OR as  y-1  and  y-1  are consecutive even numbers, thus one of them must be multiple of 4). Sufficient.

Answer: B.

Pleas use "^" for powers, and formating for formulas.

zisis · Answer

my method

1. y(y+1)  is div by 10

therefore if y is div by 10 (y^3 -y) is div by 4 BUT if y+1 is div by 10 therefore y= 9, 19 etc thus y+1 is not div by 4

2. y is odd therefore is not div by 4

any better methods?

amp0201 · Answer

B for me. I believe this problem can also be solved by using prime boxes.

tt11234 · Answer

the key point to this question is to find out if y is an odd#...i pick B

psychomath · Answer

I pick B and I agree with tt11234...The key here is to pick that y is odd!

stne · Answer

answer is definitely B , as the product of 2 consecutive even numbers is divisible by 4.
There is a small typo above , it should be (y-1) and (y+1) are 2 consecutive even numbers and  not  (y-1 ) and ( y-1) are 2 consecutive even numbers ,

Hope this prevents any confusion.
Thank you.

goldfinchmonster · Answer

I think one more case is to be considered, i.e when k = 0, y = 1. Even then 0/4 = 0 a integer. B will remain the answer

HKD1710 · Answer

If  y  is an integer greater than 0, is ( y^3  -  y ) divisible by 4?

(1)  y^2  +  y  is divisible by 10.

(2) For a certain integer  k ,  y  = 2 k  + 1

Bunuel · Answer

Merging topics. Please refer to the discussion above.

coolkl · Answer

Hello Bunnel or GMATCLUB members,

For Statement 2 we say since y is odd means y-1 is even and y+1 is even, so the given statement is div by 4. But consider if y = 1 since it is given y>0.
Now y-1 is 0 and y+1 = 2. Could this be a valid case ? Then the answer will be C. Request your help?

coolkl · Answer

I got my answer, if y =1 then (y-1)y(y+1) is 0 and 0 div by 4 is still 0. This is good question.

profileusername · Answer

I got to understand that 'y' is odd as given in statement (2) but if y=1, the expression given would become zero. So it shouldn't be considered as divisible by 4.

Bunuel · Answer

You should brush up fundamentals. ZERO: 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Check more here: https://gmatclub.com/forum/number-proper ... 74996.html

bumpbot · Answer

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If y > 0, is (y^3 – y) divisible by 4?

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If y > 0, is (y^3 – y) divisible by 4?

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