If v^2 – t^2 = 24, then w^2 – u^2 =

\(v^2 – t^2 = 24\)
So, (v+t)(v-t) = 24

One way to get the product of 24 is 2*12
We can use the equations
v+t = 12
v-t = 2
Solving these two equations, we get v=7 and t=5
Since the letters represent consecutive integers, we can say that w = 8 and u = 6

Hence, the value of the expression becomes \(w^2 – u^2 = 8^2 - 6^2 = 64-36 = 28\)(Option B)

shashankism - can you please elaborate your calculations?

Anyway this is my approach: v^2-t^2=24 ----> (v-t)(v+t)=24. As there is one number between v and t (u) the difference between v and t is necessarily even, whether v and t are odd or even numbers (odd-odd=even, even-even=even). So 24 is build from a multiplication of two even numbers. The options for the multiplications are 2 and 12 as well as 4 and 6. As we checking the options we revealed that 4 and 6 is impossible because if (v-t)=4 and (v+t)=6 ----> v=5. It means that t=3 and it doesn't satisfy the equation (5^2-3^2 equal 16 not 24). So the only option is 2 and 12. When we add the equations (v-t=2 and v+2=12) we get that v=7 and t=5. It satisfies the equation in the question (7^2-5^2=24). Now, as we deal with consecutive numbers, we can also calculate to value of u and w (6 and 8) and solve the question: 8^2-6^2 ----> 64-36 ----> 28.

Answer: A

Since t, u, v .... represent consecutive integers... the difference between them is 1 and hence difference between v and t is 2.
Simply v-t = 2
u = t+1
v = t+2
w = t+3
x = t+4
y = t+5
z = t+6

I donno why are u even trying to decode from the factors of 24,... This step is not at all required...

Thanks! Your approach is much easier. You mentioned mistakenly that t+t+2=24 instead of t+t+2=12


Sent from my iPhone using GMAT Club Forum

Yes t+t+2 = 12... I have done a mistake there.. Edited in the original solution..

assume t = x -----1
as these are consecutive integer ..
v = x + 2
t = x

v^2 - t ^2 = 24-------2
replacing the values in equation 2
(x+2-x)(x+2+x) = 24
x+1 = 6
x = 5
t= 5-----------------------3

using 3 we will get

w = 8
u=6

8^2 - 6^2 = 28 ...

shashankism, maybe I need more coffee, but I don't follow how you got from:

(v-t)(v+t) = 24, to

2(v+t) = 24

Please explain?

It does. Beautifully explained. Thanks!

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