BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Which of the following expressions can be written as an inte

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 93
Joined: Mon Apr 25, 2016 2:22 pm
Thanked: 1 times
Followed by:1 members

Which of the following expressions can be written as an inte

by boomgoesthegmat » Wed May 04, 2016 4:35 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Which of the following expressions can be written as an integer?

I. (sqrt82 + sqrt82)^2
II. (82)(sqrt82)
III. (sqrt82)(sqrt82)/82

A) None
B) I only
C) III only
D) 1 and II
E) I and III

OA: E
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed May 04, 2016 12:14 pm
boomgoesthegmat wrote:Which of the following expressions can be written as an integer?

I. (√82 + √82)²
II. (82)(√82)
III. (√82)(√82)/82

A) None
B) I only
C) III only
D) I and II
E) I and III

OA: E
We'll use the fact that (√82)(√82) = 82

I. (√82 + √82)² = (2√82)² = (2√82)(2√82) = (2)(2)(√82)(√82) = (4)(82) = some integer
III. (√82)(√82)/82 = 82/82 = 1

NOTE: As we're checking expressions, we should also be checking the answer choices.
Since I and III both work, the correct answer must be E, since there's no option for all 3 to be true.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8083
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Wed Dec 20, 2017 10:53 am
boomgoesthegmat wrote:Which of the following expressions can be written as an integer?

I. (sqrt82 + sqrt82)^2
II. (82)(sqrt82)
III. (sqrt82)(sqrt82)/82

A) None
B) I only
C) III only
D) 1 and II
E) I and III
Let's simplify each expression:

1. (√82 + √82)^2

(√82 + √82)^2 = (2√82)^2 = 4 x 82 = 328

We see that this an integer.

2. 82√82

Since √82 is a non-terminating decimal, 82√82 is not an integer.

3. (√82√82)/82

(√82√82)/82 = 82/82 = 1

We see that this is an integer.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

Re: Which of the following expressions can be written as an inte

by [email protected] » Mon Apr 19, 2021 8:34 pm
Hi All,

We’re asked which of the following Roman Numerals can be written as an INTEGER.

While Roman Numeral questions can sometimes be time-consuming, this one is relatively straight-forward and is built on a couple of Number Property rules that can help you to avoid doing heavy calculations. You also do not need to consider all 3 Roman Numerals to answer it…

First, it’s worth noting that 82 is NOT a Perfect Square (if you know your Perfect Squares at this point, then you know that 9x9 = 81 and 10x10 = 100 are the two Squares just ‘below’ and ‘above’ 82, respectively).

I.

Adding any two identical terms together can be rewritten as 2(that term). For example, 3 + 3 = 2(3)…. X + X = 2(X)…. Etc.

Here, we’re adding root-82 to root-82, so that’s 2(root-82). Squaring that term would give us (2)(2)(82)… which is clearly an INTEGER (it’s 328, but you don’t actually have to do that math).

III.

Here, we are multiplying the same Square Root against itself – and any time you do that, you end up with the original integer. For example (root-4)(root-4) = (2)(2) = 4… (root-5)(root-5) = 5… Etc.

Thus, we would end up with 82 in the numerator and 82 in the denominator – and 82/82 = 1. This also is clearly an INTEGER.

Based on how the Answers are written, we can stop working.

Final Answer: E

GMAT Assassins aren’t born, they’re made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1