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

Redeem

Rank the following quantities in order, from smallest to biggest.

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1622
Joined: Thu Mar 01, 2018 7:22 am
Followed by:2 members

Rank the following quantities in order, from smallest to biggest.

by Gmat_mission » Fri Feb 11, 2022 8:42 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Rank the following quantities in order, from smallest to biggest.

I. \(2^{60}\)

II. \((2\sqrt2)^{35}\)

III. \(3^{42}\)

(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) II, III, I
(E) III, II, I

Answer: C

Source: Magoosh
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

Re: Rank the following quantities in order, from smallest to biggest.

by Ian Stewart » Fri Feb 11, 2022 2:59 pm
2 √2 = 2 * 2^(1/2) = 2^(3/2), so we can rewrite item II:

(2 √2)^35 = (2^3/2)^35 = 2^105/2

and since 105/2 < 60, this is less than 2^60.

To compare 2^60 and 3^42, we can notice that 2^60 = (2^3)^20 = 8^20, and 3^42 = (3^2)^21 = 9^21, and since 8^20 has both a smaller base and smaller exponent than 9^21, it is the smaller number (here using the fact that the bases are positive integers), so the answer is II, I, III.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Post new topic Post Reply
• Page 1 of 1