Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In this question, wouldn't statements 1 and 2 together be insufficient?

Question: Is x² - y² divisible by 8?

1. x and y are even integers

2. x + y is divisible by 8

According to the answer key, the correct answer is C, but aren't the statements together insufficient? Consider:

The answer is yes if, for example x=6 and y=2 because (6+2)(6-2) is divisible by 8

The answer is no if x=4 and y=4 because (4+4)(4-4) is not divisible by 8

Hi Fluke,

If it was mentioned in the question itself that x and y are integers (not necessarily even integers), Option B would have sufficed right?
_________________

In this question, wouldn't statements 1 and 2 together be insufficient?

Question: Is x² - y² divisible by 8?

1. x and y are even integers

2. x + y is divisible by 8

According to the answer key, the correct answer is C, but aren't the statements together insufficient? Consider:

The answer is yes if, for example x=6 and y=2 because (6+2)(6-2) is divisible by 8

The answer is no if x=4 and y=4 because (4+4)(4-4) is not divisible by 8

Infamous "0" is a multiple of everything "Or" 0 is divisible by everything but itself "Or" every known number is a factor of "0".

Thus, 0 is divisible by 8. 0 when divided by 8 leaves a remainder 0. "0/8=0"

Still Didn't get you fluke isn't statement 2 sufficient as x² - y²=(x+y)(x-y) now if (x+y) is divisible by 8 then whole term x² - y² will also be divisible by 8

did not understand how st 1 is useful
_________________

WarLocK _____________________________________________________________________________ The War is oNNNNNNNNNNNNN for 720+ see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html do not hesitate me giving kudos if you like my post.

We are not told that x and y are integers. If x=3/4 and y= 3/2, statement B alone will not suffice. We need to be sure that x and y are integers. Thats what statement 1 tells us and thats how it is useful
_________________

Still Didn't get you fluke isn't statement 2 sufficient as x² - y²=(x+y)(x-y) now if (x+y) is divisible by 8 then whole term x² - y² will also be divisible by 8

did not understand how st 1 is useful

I agree with gmatpapa.

x=6.8 y=1.2

x+y=6.8+1.2=8 x-y=6.8-1.2=5.6

x^2-y^2=(x+y)(x-y)=8*5.6=44.8

44.8 is not divisible by 8

44.8/8 = 448/80=28/5 will leave a remainder of 3.

If both x and y were even integers, then x+y=even integer, x-y=even integer And (x+y) is divisible by 8, then (x+y)/8= integer

\frac{x^2-y^2}{8}=\frac{(x+y)(x-y)}{8} \frac{x+y}{8}*(x-y)=integer*integer=integer Thus 8 will divide x^2-y^2 leaving an integer as quotient and no remainder. Ans: "C" *************

can be rephrased as Is (x-y)(x+y) divisible by 8 where x and y are integers. Is this correct?

Why did you add the extra bit "where x and y are integers". I am not able to gather your thought process. I would just rephrase it as, "Is (x-y)(x+y) divisible by 8?".
_________________

Is x² - y² divisible by 8? I think the necessary condition (x+y)or(x-y) or their product divisible by 8 is not sufficient to answer the question. We also need the condition - Is x and y integers? to conclusively answer.

yes to both questions - the answer is yes yes and no to questions - the answer is no no and no to questions - the answer is no

I meant we need answers to two questions to answer this question - Is x² - y² divisible by 8? Isnt it?

Is x² - y² divisible by 8? I think the necessary condition (x+y)or(x-y) or their product divisible by 8 is not sufficient to answer the question. We also need the condition - Is x and y integers? to conclusively answer.

yes to both questions - the answer is yes yes and no to questions - the answer is no no and no to questions - the answer is no

I meant we need answers to two questions to answer this question - Is x² - y² divisible by 8? Isnt it?

I see. Yes, correct. I somehow thought that you were trying to rephrase the question stem. Gotcha.
_________________

Re: m15 question 23 [#permalink]
21 Feb 2013, 03:32

Expert's post

Sachin9 wrote:

Why is B not sufficient...

x^2-y^2 =(x+y)(x-y)

If x+y is divisible by 8 .. so is (x+y)(x-y).

Kindly help..

Is x^2 - y^2 divisible by 8?

(1) x and y are even integers. Clearly insufficient, consider x=y=0 for an YES answer and x=2 and y=0 for a NO answer.

(2) x + y is divisible by 8 --> x^2 - y^2=(x+y)(x-y), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that x and y are integers. If x=4.8 and y=3.2, x+y is divisible by 8, BUT x^2 - y^2 is not. Not sufficient.

(1)+(2) x and y integers. x+y divisible by 8. Hence (x+y)(x-y) is divisible by 8. Sufficient.

Re: m15 question 23 [#permalink]
21 Feb 2013, 04:16

Bunuel wrote:

Sachin9 wrote:

Why is B not sufficient...

x^2-y^2 =(x+y)(x-y)

If x+y is divisible by 8 .. so is (x+y)(x-y).

Kindly help..

Is x^2 - y^2 divisible by 8?

(1) x and y are even integers. Clearly insufficient, consider x=y=0 for an YES answer and x=2 and y=0 for a NO answer.

(2) x + y is divisible by 8 --> x^2 - y^2=(x+y)(x-y), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that x and y are integers. If x=4.8 and y=3.2, x+y is divisible by 8, BUT x^2 - y^2 is not. Not sufficient.

(1)+(2) x and y integers. x+y divisible by 8. Hence (x+y)(x-y) is divisible by 8. Sufficient.

Answer: C.

x^2-y^2 is ultimately (x+y)(x-y) .. So irrespective of whether x and y are integers or not.. if (x+y) is divisible by 8 , why can't (x+y)* ( x-y) be divisible by 8?

What am I missing?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Re: m15 question 23 [#permalink]
21 Feb 2013, 04:20

Expert's post

Sachin9 wrote:

Bunuel wrote:

Sachin9 wrote:

Why is B not sufficient...

x^2-y^2 =(x+y)(x-y)

If x+y is divisible by 8 .. so is (x+y)(x-y).

Kindly help..

Is x^2 - y^2 divisible by 8?

(1) x and y are even integers. Clearly insufficient, consider x=y=0 for an YES answer and x=2 and y=0 for a NO answer.

(2) x + y is divisible by 8 --> x^2 - y^2=(x+y)(x-y), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that x and y are integers. If x=4.8 and y=3.2, x+y is divisible by 8, BUT x^2 - y^2 is not. Not sufficient.

(1)+(2) x and y integers. x+y divisible by 8. Hence (x+y)(x-y) is divisible by 8. Sufficient.

Answer: C.

x^2-y^2 is ultimately (x+y)(x-y) .. So irrespective of whether x and y are integers or not.. if (x+y) is divisible by 8 , why can't (x+y)* ( x-y) be divisible by 8?

What am I missing?

In my post above there is an example for which x^2 - y^2 is NOT divisible by 8 (x=4.8 and y=3.2) because it's not an integer at all.
_________________

Re: m15 question 23 [#permalink]
22 Feb 2013, 01:36

Bunuel wrote:

No. x^2 - y^2 can be divisible by 8 even if x and y are not integers. For example, x=7.5 and y=0.5.

ok. so no such rule for divisibility as such.. we gotto plug in numbers and check .. numbers to be plugged in would depend on the scope of the variables..
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Re: m15 question 23 [#permalink]
22 Feb 2013, 02:09

Is x² - y² divisible by 8?

1. x and y are even integers

2. x + y is divisible by 8

It is a Yes No Data Sufficiency question wherein you should try to disprove the statements rather than prove them. To disprove a statement there should be at least two values which will satisfy and not satisfy the condition in the question or simply you need a yes and a no from the statement.

Lets see:

Statement (1): Lets substitute for x and y Let us say x = 4 and y = 2 (Satisfies the statement) Putting it in x² - y² we get, 12 which is not divisible by 8, hence we get a 'NO'.

Now lets try for a yes, let us say x = 16 and y = 8(Satisfies the statement) x² - y² = 192, which is divisible by 8, so we have a 'YES'

Since we have a yes and a no so this statement is not sufficient.

Statement (2): Let us do the same for statement 2 X = 6 and Y = 2 (Satisfies the statement) x² - y² = 32, so we get a YES

X = 7.6 and Y = 0.4 x² - y² = 57.6, hence it is not divisible by 8

If we combine both we get the answer as it tells us that x and y are integers.
_________________

Pushpinder Gill

gmatclubot

Re: m15 question 23
[#permalink]
22 Feb 2013, 02:09