For Consecutive integers x, y and z, where x y z, which of the

Question

For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of  (x^2 - y^2)*(y^2 - z^2)  ?

A) 63
B) 99
C) 195
D) 276
E) 323

Senthil1981 · Accepted Answer

Plz let me know,method to solve these kind of questions

The question mentions that the numbers are consecutive and  x >y > z 
so first simplify  (x^2−y^2)∗(y^2−z^2) = (x - y) * (x + y) * (y - z) * (y + z)  and since  x > y > z , x - y = 1  and  y - z = 1 
So what remains is  (x +y ) * (y + z)  and since the numbers are consecutive,  x +y  and  y + z  has to odd, so only option which is even is D CANNOT be value.

chetan2u · Answer

This is too simple....even n odd
Say if I gave you D as 209.. and A as 35 and rest all same
What will be the answer

Nevernevergiveup · Answer

OE:

Perhaps we should list a few of our squares here: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169. OK, that should take us far enough. Now, since we just need the differences between consecutive squares, we can just consider the intervals between values listed above: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25. Upon noticing that these intervals are only odd, one must conclude that a product of two of them must be odd and the answer is clearly D.

chetan2u · Answer

The main logic to this Q is that the answer has to be a multiple of CONSECUTIVE odd integers....
Incase no choice was EVEN, we would be looking into this aspect

Nevernevergiveup · Answer

Also we can derive whole wuqation  (x +y ) * (y + z)  in terms of x as  (2x-1)(2x-3)  since  y=x-1  and  z=y-1=x-2

we can easily note that  (2n + k)  where k is any odd number indicates an odd number.
Hence product of two odd numbers is an odd number.

azamaka · Answer

2 ways:
1) x-odd y-even z-odd  (odd^2-even^2)^(even^2-odd^2) = even 
2) x-even y-odd z-even  (even^2-odd^2)^(odd^2-even^2) =even

The only even answer we have is D) 276

Jurassic · Answer

Continuing from Senthil1981's solution, (x+y)(y+z) can be represented in terms of y as (y+1+y)(y+y-1)--->(2y+1)(2y-1)--->4y^2-1
Now equate 4y^2-1 to each answer option and check if you are getting a valid integer value for y. It will work for all options excluding 276.Hence, D is the answer.

EMPOWERgmatRichC · Answer

Hi All,

GMAT questions are almost always built around patterns - even if you don't realize that the pattern is there, you can probably do a bit of 'brute force' work and define the pattern. By extension, if you know the pattern, then you should be able to use that knowledge to your advantage to either answer the question immediately (or do another step or two of work to get the answer).

Here, we're given some specific facts to work with: 
1) X, Y and Z are CONSECUTIVE integers 
2) X > Y > Z

We're asked for what CANNOT be the value of (X^2 - Y^2)(Y^2 - Z^2).

Let's TEST VALUES and see if a pattern emerges...

IF... X = 3, Y = 2, Z = 1.... 
(9 - 4)(4 - 1) = (5)(3) = 15

So "15" is a possible answer. Also note that we ended up multiplying two ODD numbers together... Let's try another TEST....

IF... X = 4, Y = 3, Z = 2.... 
(16 - 9)(9 - 4) = (7)(5) = 35

So "35" is a possible answer. Notice that we again ended up multiplying two ODD numbers together... That looks like a pattern. If the end result is just going to be an ODD number every time, then there's clearly an answer that CANNOT be the value...

If you're not convinced yet, then try another example (and feel free to try as many as you like - as the numbers increase, you'll eventually hit all 4 of the possible answers, at which point you'll know which answer is NOT possible.

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

akadiyan · Answer

EMPOWERgmatRichC

Understanding pattern is interesting and looks certainly quicker. Thanks much for the awesome solution.

gracie · Answer

looking at consecutive sequences 3,2,1 and 4,3,2,
(x^2-y^2)*(y^2-z^2)=(x+y)*(y+z)
because both x+y and y+z are sums of odd plus even or even plus odd integers, they must be odd
two odd factors cannot produce an even product
276 cannot be the value (x+y)*(y+z)
D

saraheja · Answer

Simple question on even/odd concept. D would be the answer

jeriiiiiii · Answer

If it involves three consecutive integers, I would like to discuss two different cases.

using numbers as substitutes is not suiatable for this question(for my personal);

use “n” to represent the three consecutive numbers instead.
then

12n+1>2n>2n-1
22n+2>2n+1>2n
----->(x^2−y^2)∗(y^2−z^2)

you can get these two
316n^2-1
416(n^2+n)+3

A:using3-->63+1=64,-->64/16=2^2.√

B:not for3, but for 4
99-3=96,96/16=6,n=2.√
.......
only D doesnt work in 34.

For Consecutive integers x, y and z, where x > y > z, which of the

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