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Senior Manager  V
Joined: 02 Jan 2017
Posts: 292
0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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6 00:00

Difficulty:   55% (hard)

Question Stats: 64% (02:03) correct 36% (02:05) wrong based on 141 sessions

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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
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15644
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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3
3
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

GMAT assassins aren't born, they're made,
Rich
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##### General Discussion
Intern  B
Joined: 19 Jan 2017
Posts: 2
Location: India
Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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1
1

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
Intern  B
Joined: 26 Dec 2016
Posts: 28
0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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EMPOWERgmatRichC wrote:
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

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

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?

Originally posted by rnz on 20 Mar 2018, 11:30.
Last edited by rnz on 20 Mar 2018, 11:34, edited 1 time in total.
Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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arkbatman wrote:

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

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,

Posted from my mobile device
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Intern  B
Joined: 01 Nov 2015
Posts: 15
Location: Russian Federation
WE: Other (Other)
0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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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.

Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8611
Location: United States (CA)
Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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1
vikasp99 wrote:
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

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

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Intern  B
Joined: 09 Mar 2018
Posts: 2
Location: India
Schools: Stern '21
GMAT 1: 650 Q47 V34 GPA: 3.2
Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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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
VP  V
Joined: 23 Feb 2015
Posts: 1335
Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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EMPOWERgmatRichC wrote:
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

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

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...
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VP  V
Joined: 23 Feb 2015
Posts: 1335
Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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ScottTargetTestPrep wrote:
vikasp99 wrote:
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

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

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__
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

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Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: 0 < x < y, and x and y are consecutive integers. If the difference bet  [#permalink]

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ScottTargetTestPrep wrote:
vikasp99 wrote:
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

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

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__

Notice that we are also told that 0 < x < y, so y = x + 1. Re: 0 < x < y, and x and y are consecutive integers. If the difference bet   [#permalink] 02 Sep 2018, 21:19
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