1001^2 - 999^2 / 101^2 - 99^2 ?
a) 10
b) 20
c) 40
d) 80
e) 100
Answer is a. Can someone please explain it.
Thanks,
Vito
a) 10
b) 20
c) 40
d) 80
e) 100
Answer is a. Can someone please explain it.
Thanks,
Vito
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This is from the GMAT Prep.tonker wrote:1001^2 - 999^2 / 101^2 - 99^2 ?
a) 10
b) 20
c) 40
d) 80
e) 100
Answer is a. Can someone please explain it.
Thanks,
Vito
Based on (a + b)^2 = a^2 + b^2 + 2*a*b
and (a - b)^2 = a^2 + b^2 - 2*a*b:
(1001^2 - 999^2) / (101^2 - 99^2)
= (1000 + 1)^2 - (1000 - 1)^2 / (100 + 1)^2 - (100 - 1)^2
= (1000^2 + 1^2 + 2*1*1000) - (1000^2 + 1^2 - 2*1*1000) / (100^2 + 1^2 + 2*1*100) - (100^2 + 1^2 - 2*1*100)
= 4000/400
= 10
and (a - b)^2 = a^2 + b^2 - 2*a*b:
(1001^2 - 999^2) / (101^2 - 99^2)
= (1000 + 1)^2 - (1000 - 1)^2 / (100 + 1)^2 - (100 - 1)^2
= (1000^2 + 1^2 + 2*1*1000) - (1000^2 + 1^2 - 2*1*1000) / (100^2 + 1^2 + 2*1*100) - (100^2 + 1^2 - 2*1*100)
= 4000/400
= 10
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Alternatively, using Raj's suggestion (this is the shortcut):
1001^2 - 999^2 / 101^2 - 99^2
(1001 + 999)(1001 - 999) / (101 + 99)(101-99)
(2000)(2)
(200)(2)
cross off 2's, cross off two zero's each from top and bottom
20/2
10
1001^2 - 999^2 / 101^2 - 99^2
(1001 + 999)(1001 - 999) / (101 + 99)(101-99)
(2000)(2)
(200)(2)
cross off 2's, cross off two zero's each from top and bottom
20/2
10
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Stacey Koprince
GMAT Instructor
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Manhattan GMAT
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Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
In solving this question, let us first recall the algebraic equation
a^2 - b^2 = (a-b)(a+b)
(1001^2 - 999^2) / (101^2 - 99^2)
solving the numerator first,
1001^2 - 999^2 = (1001-999)(1001+999)
=(2)(2000)
=4000
let solve the denominator
101^2 - 99^2 = (101-99)(101+99)
=2*200
=400
Solving mathematically using the division method,
numerator/denominator= 4000/400
=10
we got 10 as the answer which is option A
a^2 - b^2 = (a-b)(a+b)
(1001^2 - 999^2) / (101^2 - 99^2)
solving the numerator first,
1001^2 - 999^2 = (1001-999)(1001+999)
=(2)(2000)
=4000
let solve the denominator
101^2 - 99^2 = (101-99)(101+99)
=2*200
=400
Solving mathematically using the division method,
numerator/denominator= 4000/400
=10
we got 10 as the answer which is option A
GMAT/MBA Expert
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Scott@TargetTestPrep
- GMAT Instructor
- Posts: 8139
- Location: Los Angeles, CA
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We can see that both the numerator and denominator are differences of two squares. Therefore, the numerator can be factored and simplified as:
(1001 - 999)(1001 + 999) = 2(2000) = 4000
Similarly, the denominator can be factored and simplified as:
(101 - 99)(101 + 99) = 2(200) = 400
Therefore, the quotient is 4000/400 = 10.
Answer: A
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