It is currently 10 Aug 2020, 11:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# 15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63)

Author Message
TAGS:
GRE Instructor
Joined: 10 Apr 2015
Posts: 3657
Followers: 141

Kudos [?]: 4205 [2] , given: 67

15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63) [#permalink]  06 Nov 2019, 15:03
2
KUDOS
Expert's post
00:00

Question Stats:

81% (01:38) correct 18% (03:00) wrong based on 11 sessions
$$15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63)=$$

A) 53
B) 83
C) 91
D) 93
E) 105
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll love my GRE prep course!

GRE Instructor
Joined: 10 Apr 2015
Posts: 3657
Followers: 141

Kudos [?]: 4205 [2] , given: 67

Re: 15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63) [#permalink]  24 Mar 2020, 09:01
2
KUDOS
Expert's post
GreenlightTestPrep wrote:
$$15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63)=$$

A) 53
B) 83
C) 91
D) 93
E) 105

Key Properties:
#1: $$(x + y)^2 = x^2 + 2xy + y^2$$
#2: $$(x - y)^2 = x^2 - 2xy + y^2$$
#3: $$x^2-y^2 = (x+y)(x-y)$$

Given: $$15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63)$$

Notice that 15 appears in two terms, and 63 appears in two terms.
Also, if we recognize that 54 = (2)(27), we see that 27 appears twice.
And, if we recognize that 44 = (2)(22), we see that 22 appears twice.

Here's what I mean: $$15^2 - 63^2 + 27^2 - 22^2 + (2)(27)(15) + (2)(63)(22)$$

Let's group the similar terms to get: $$27^2 + (2)(27)(15) +15^2 - 63^2 + (2)(63)(22)-22^2$$
Rewrite to get: $$[27^2 + (2)(27)(15) +15^2] - [63^2 - (2)(63)(22)+22^2]$$

Notice that $$27^2 + (2)(27)(15) +15^2$$ looks a lot like the expansion in key property #1, and $$63^2 - (2)(63)(22)+22^2$$ looks a lot like the expansion in key property #2

So, we can factor them as follows: $$(27+15)^2 - (63-22)^2$$
Simplify: $$42^2 – 41^2$$ [aha! A difference of squares!!]
Use property #3 to factor the expression: $$(42+41)(42-41)$$
Simplify: $$(83)(1)$$
Evaluate: $$83$$

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll love my GRE prep course!

Re: 15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63)   [#permalink] 24 Mar 2020, 09:01
Display posts from previous: Sort by