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27 Feb 2017, 01:27
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:52) correct
29%
(02:07)
wrong
based on 477
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
(A) 6,100
(B) 6,101
(C) 12,200
(D) 12,201
(E) 24,402
27 Feb 2017, 21:57
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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:
GMAT assassins aren't born, they're made,
Rich
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:
GMAT assassins aren't born, they're made,
Rich
27 Feb 2017, 01:34
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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
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
