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Question

0 < x < y, and x and y are consecutive integers. If the difference between x^2 and y^2 is 12,201, then what is the value of x?

(A) 6,100

(B) 6,101

(C) 12,200

(D) 12,201

(E) 24,402

EMPOWERgmatRichC · Accepted Answer

Hi vikasp99,

This question can be solved in a couple of different ways. It's also built around some specific Number Properties, so if you're not sure how to approach the question, you can take advantage of those patterns and take a great guess.

We're told that X and Y are CONSECUTIVE INTEGERS (0 < X < Y) and that Y^2 - X^2 = 12,201. We're asked for the value of X.

To start, it's interesting that the DIFFERENCE ends in a 1. When subtracting the squares of consecutive integers, there are only a couple of ways that this can occur:

Y ends in a 1 and X ends in a 0 
Y ends in a 6 and X ends in a 5

From the answer choices, we can clearly see that it's the first option - and that the correct answer is either Answer A or Answer C. If you're not sure what to do next, then you could guess and move on. However, if you want to continue working, you don't actually have to square two big numbers to find the solution to this question.

Since the two variables are consecutive, we can rewrite Y as (X + 1), so the original equation can be written as...

(X+1)^2 - X^2 = 12,201
X^2 + 2X + 1 - X^2 = 12,201
2X + 1 = 12,201
2X = 12,200
X = 6,100

Final Answer:  A

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

arkbatman · Answer

Answer: (A)

Since x and y are consecutive integers you can take y=x+1.

So y^2-x^2=2x+1=12201
2x=12200
x=6100.

Sent from my Nexus 5 using  GMAT Club Forum mobile app

rnz · Answer

Hi,  EMPOWERgmatRichC  When I first did the problem, I didn't actually come up with an answer, but did end up with a 61 while trying to figure out an approach. So I figured out that it had to be y^2 - x^2 = 12,201. So, I simplified 12,201 to 12,200 to make it more manageable (without doing the algebra). I then divided 12,200 by 2 which gave me 6,100 (just because I needed to try something). I thought this was a trick or some flaw in my thinking so I actually eliminated that choice. Was I just lucky in getting the 6,100 or is there an avenue to the solution somewhere in that train of thought without realizing the substitution method of y=x+1?

Gladiator59 · Answer

Another way of factoring could be..

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

Since y = x+1

This becomes 2x + 1 = 12201
2x = 12200
x = 6100.

Best,
Gladi

Posted from my mobile device

UncleFrodo · Answer

or another way:
(x-y)*(x+y)= 12 201
(x-y) = 12 201 - which is impossible because x-y= -1 (consecutive integers) and x<y
(x+y) = 12 201 - it is possible. Hence we must look at answer choices where C, D, E we can easily eliminate

We have A (6 100) and B (6 101), well it is not a big deal to understand that only A (6 100) suits to our problem.

A is the answer.

ScottTargetTestPrep · Answer

Since x and y are consecutive integers, we can let y = x + 1; thus:

(x + 1)^2 - x^2 = 12,201

x^2 + 2x + 1 - x^2 = 12,201

2x + 1 = 12,201

2x = 12,200

x = 6,100

Answer: A

pushkar633 · Answer

Sum of 2 consecutive numbers is always equal to the difference of their Squares. 
This is always true.

So in this case sum should be equal to 12,201. 
out of the options, all the options are greater than 12,201 except for a,b and c.
and since the numbers are consecutive, the numbers have to be 6,100 and 6,101

Since it is given that x<y, therefore, x=6,100

Ans - A

TheUltimateWinner · Answer

Hi  rich , hope u are well. I am very glad to have your explanation-your explanation is always fantastic! May I have another shortcut way, please?
Thanks...

TheUltimateWinner · Answer

i'm a bit confused about the  bold  part above! if x and y are consecutive integers, we can  also  let x = y + 1, right?
Thanks__

Bunuel · Answer

Notice that we are also told that 0 <  x < y , so y = x + 1.

MathRevolution · Answer

0 (y-x)(y+x) = 12201 => (x+1-x)(x+1+x) = 12201 => 1* (2x+1) = 12201 => 2x+1 = 12201 => 2x = 12200 => x = 6100 Answer A

hiranmay · Answer

0 < x < y, and x and y are consecutive integers. If the difference between x^2 and y^2 is 12,201, then what is the value of x?

(A) 6,100 --> correct: 0 < x < y, and x and y are consecutive integers i.e. y=x+1 >=2 => y+x=(x+1)+x =2x+1 & y-x=1, \(y^2-x^2=12201 => (y+x)(y-x)=12201 => (2x+1)*1=12201=>2x=12200=>x=12200/2=6100(\)

(B) 6,101

(C) 12,200

(D) 12,201

(E) 24,402

Kinshook · Answer

Given: 0 < x < y, and x and y are consecutive integers.
Asked: If the difference between x^2 and y^2 is 12,201, then what is the value of x?

y = x + 1
y^2 - x^2 = 12201
(x+1)^2 - x^2 = 12201
2x + 1 = 12201
x = 6100

IMO A

bumpbot · Answer

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0 < x < y, and x and y are consecutive integers. If the difference bet

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