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# (20^2 - 18^2) - (19^2 - 17^2)?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
(20^2 - 18^2) - (19^2 - 17^2)?  [#permalink]

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16 Aug 2017, 01:04
1
1
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:13) correct 12% (01:42) wrong based on 69 sessions

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$$(20^2 - 18^2) - (19^2 - 17^2)$$?

A. 4
B. 36
C. 38
D. 76
E. 224

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Joined: 19 Apr 2017
Posts: 11
Concentration: Strategy, Finance
Re: (20^2 - 18^2) - (19^2 - 17^2)?  [#permalink]

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16 Aug 2017, 01:11
2
=(20+18)(20-18)-(19+17)(19-17)

=(38*2)-(36*2)
=76-72
=4
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Re: (20^2 - 18^2) - (19^2 - 17^2)?  [#permalink]

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16 Aug 2017, 04:10
2
$$(20^2 - 18^2) - (19^2 - 17^2)$$
= (20+18)(20-18)-(19+17)(19-17)
=38*2-36*2
=4

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(20^2 - 18^2) - (19^2 - 17^2)?  [#permalink]

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16 Aug 2017, 05:23
Formula used:(a + b)^2 = a^2 + 2*a*b + b^2

We have been asked to find the value of the expression $$(20^2 - 18^2) - (19^2 - 17^2)$$

$$= ((18+2)^2 - 18^2) - ((17+2)^2 - 17^2)$$
$$= (18^2 +2^2 + 2(2)(18) - 18^2) - (17^2 + 2^2 + 2(2)(17) - 17^2)$$
$$= (18^2 +2^2 + 2(2)(18) - 18^2) - (17^2 + 2^2 + 2(2)(17) - 17^2)$$
Cancelling all common terms, $$= 4*18 - 4*17 = 72 - 68 = 4$$(Option A)
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(20^2 - 18^2) - (19^2 - 17^2)?  [#permalink]

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16 Aug 2017, 06:01
1
Bunuel wrote:
$$(20^2 - 18^2) - (19^2 - 17^2)$$?

A. 4
B. 36
C. 38
D. 76
E. 224

Can be solved using the formula : $$a^2 -b^2 = (a+b)(a-b)$$

$$(20^2 - 18^2) - (19^2 - 17^2)$$

$$(20 - 18)(20+18) - (19 - 17)(19+17)$$

$$(2)(38) - (2)(36)$$

$$2(38 - 36)$$

$$2(2) = 4$$

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Re: (20^2 - 18^2) - (19^2 - 17^2)?  [#permalink]

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26 Jan 2019, 00:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: (20^2 - 18^2) - (19^2 - 17^2)?   [#permalink] 26 Jan 2019, 00:27
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