Target question: Is x² − y² divisible by 8?rakeshd347 wrote:Is x² − y² divisible by 8?
(1) x and y are even integers.
(2) x+y is divisible by 8.
To be honest, I first thought the correct answer was B, but then I realized that I had assumed that x and y are integers. If x and y are not necessarily integers, then statement B is not sufficient.abhi.iitb wrote:Hello Brent,
I think the answer for this Q is B, since x+ y is always a factor of x2-y2 so statement B is sufficient to answer this question. Infact, case b in statement 2 is divisible by 8 if we actually perform the calculation.
Please tell me if I am missing anything here.
Abhishek
Divisible by 8 means answer should be integer. Here, answer is not an integer!kuzzden wrote:Case b: x = 7.9 and y = 0.1
Here, x² - y² = 62.4
We may say that 62.4 is divisible by 8, but the answer is not an integer, since there is no requirement that either x or y or both be integers
So ans is B. Or am I missing smth?
This is a tricky question and the trap answer is crafted nicely. If you don't give due care to whether x and y are integer you will definitely get it wrong. I initially though x+y is divisible by 8 done bang. Then thought it can't be so easy let me think and then came across this trap.abhi.iitb wrote:I totally agree with Kuzzden,
@riz_gmat: I believe divisibility by 8 means that we get terminating no if we divide 62.4 with 8 which is the case here. Suppose we had 62.5 instead of 62.4 then we would have said that number is not divisible by 8 since the dividend comes out to be non-terminating.
Experts, seek your guidance on this concept.
abhi.iitb wrote:I totally agree with Kuzzden,
@riz_gmat: I believe divisibility by 8 means that we get terminating no if we divide 62.4 with 8 which is the case here. Suppose we had 62.5 instead of 62.4 then we would have said that number is not divisible by 8 since the dividend comes out to be non-terminating.
Experts, seek your guidance on this concept.
I agree with you "riz_gmat" .. if we go on dividing into decimals than nearly all numbers are divisible to every other number; we must restrict to Quotient Integerriz_gmat wrote:abhi.iitb wrote:I totally agree with Kuzzden,
@riz_gmat: I believe divisibility by 8 means that we get terminating no if we divide 62.4 with 8 which is the case here. Suppose we had 62.5 instead of 62.4 then we would have said that number is not divisible by 8 since the dividend comes out to be non-terminating.
Experts, seek your guidance on this concept.
According to my knowledge, When GMAT asks whether x is divisible y, they mean "when x is divided by y the remainder is zero" . In this case we have decimal point in our ans, and we use decimal point while dividing, when we have a non zero remainder.
Experts, kindly clarify!
If we divide any terminating decimal by 8, the result (quotient) will always be terminating.abhi.iitb wrote:I totally agree with Kuzzden,
@riz_gmat: I believe divisibility by 8 means that we get terminating no if we divide 62.4 with 8 which is the case here. Suppose we had 62.5 instead of 62.4 then we would have said that number is not divisible by 8 since the dividend comes out to be non-terminating.
Experts, seek your guidance on this concept.
You'll find that most (if not all) GMAT divisibility questions involve integers.riz_gmat wrote:abhi.iitb wrote:I totally agree with Kuzzden,
@riz_gmat: I believe divisibility by 8 means that we get terminating no if we divide 62.4 with 8 which is the case here. Suppose we had 62.5 instead of 62.4 then we would have said that number is not divisible by 8 since the dividend comes out to be non-terminating.
Experts, seek your guidance on this concept.
According to my knowledge, When GMAT asks whether x is divisible y, they mean "when x is divided by y the remainder is zero" . In this case we have decimal point in our ans, and we use decimal point while dividing, when we have a non zero remainder.
Experts, kindly clarify!
I agree with Brent that it not likely to an gmat question. However, it is a good question to gain knowledge and some take away from this. Don't assume numbers integer until unless it is mentioned.Brent@GMATPrepNow wrote:You'll find that most (if not all) GMAT divisibility questions involve integers.riz_gmat wrote:abhi.iitb wrote:I totally agree with Kuzzden,
@riz_gmat: I believe divisibility by 8 means that we get terminating no if we divide 62.4 with 8 which is the case here. Suppose we had 62.5 instead of 62.4 then we would have said that number is not divisible by 8 since the dividend comes out to be non-terminating.
Experts, seek your guidance on this concept.
According to my knowledge, When GMAT asks whether x is divisible y, they mean "when x is divided by y the remainder is zero" . In this case we have decimal point in our ans, and we use decimal point while dividing, when we have a non zero remainder.
Experts, kindly clarify!
In fact, the OG defines divisibility (divisors) as follows:
If x and y are integers and x ≠0, then x is a divisor (factor) of y provided that y = xn for some integer n.
So, you won't be asked whether some non-integer is divisible by an integer.
Given all of this, I'd say that it's unlikely that this could ever be an official GMAT question.
Cheers,
Brent
