GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jun 2018, 00:54

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If 0 < a < 1, which of the following is the greatest?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46291
If 0 < a < 1, which of the following is the greatest? [#permalink]

### Show Tags

10 Sep 2017, 05:13
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

64% (01:06) correct 36% (01:21) wrong based on 120 sessions

### HideShow timer Statistics

If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

C. $$(\frac{1}{a})^{(-2)}$$

D. $$a^{(-2)}$$

E. $$a^2$$

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82
If 0 < a < 1, which of the following is the greatest? [#permalink]

### Show Tags

10 Sep 2017, 12:55
1
Bunuel wrote:
If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

C. $$(\frac{1}{a})^{(-2)}$$

D. $$a^{(-2)}$$

E. $$a^2$$

as $$a$$ is positive and $$a<1$$, so $$\frac{1}{a}>1$$. Hence a fraction where $$a$$ is in the denominator and numerator is $$1$$ will have a value greater than $$1$$. Hence we can straight away eliminate options B, C & E as $$a$$ is in the numerator (essentially option B, C & E are same $$= a^2$$ and as it is given $$a<1$$, so squaring both sides will yield $$a^2<1$$)

Option A: can be written as $$\frac{1}{(2a)^{2}}$$ $$= \frac{1}{4a^2}$$

Option D: can be written as $$\frac{1}{a^2}$$. Multiply the numerator and the denominator by $$4$$. we get
$$\frac{4}{4a^2} > \frac{1}{4a^2}$$

Hence Option D
SC Moderator
Joined: 22 May 2016
Posts: 1759
If 0 < a < 1, which of the following is the greatest? [#permalink]

### Show Tags

14 Sep 2017, 11:09
1
Bunuel wrote:
If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

C. $$(\frac{1}{a})^{(-2)}$$

D. $$a^{(-2)}$$

E. $$a^2$$

Let a = $$\frac{1}{4}$$, and evaluate each answer choice. Straight algebra -- reciprocals, fractions, and squares -- became too tangled.

A. $$(-2a)^{(-2)}$$ --> $$\frac{1}{(-2*a)^2}$$

$$\frac{1}{(-2*\frac{1}{4})^2}$$ =

$$\frac{1}{(-\frac{1}{2})^2}$$ = $$\frac{1}{(\frac{1}{4})}$$ = 4

B. $$\frac{1}{a^{(-2)}}$$ --> $$\frac{a^2}{1^2}$$

$$a^2$$ = $$(\frac{1}{4})^2$$ =$$\frac{1}{16}$$

C.$$(\frac{1}{a})^{(-2)}$$ --> $$\frac{a^2}{1^2}$$=

$$a^2$$. Same as Answer B =$$\frac{1}{16}$$

D. $$a^{(-2)}$$--> $$\frac{1}{a^2}$$

$$\frac{1}{(\frac{1}{4})^2}$$ = $$\frac{1}{\frac{1}{16}}$$ = 16

E. $$a^2$$ = same as Answer B = $$\frac{1}{16}$$

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2773
Location: United States (CA)
Re: If 0 < a < 1, which of the following is the greatest? [#permalink]

### Show Tags

20 Sep 2017, 15:51
1
Bunuel wrote:
If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

C. $$(\frac{1}{a})^{(-2)}$$

D. $$a^{(-2)}$$

E. $$a^2$$

Since we know a is between 0 and 1, let’s let a = 1/2. Now we analyze each answer choice:

A)

[-2(1/2)]^-2 = (-1)^-2 = 1

B)

1/(1/2)^-2 = 1/(2^2) = ¼

C)

(1/(1/2))^-2 = 2^-2 = 1/4

D)

(1/2)^-2 = 2^2 = 4

E)

(1/2)^2 = 1/4

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If 0 < a < 1, which of the following is the greatest?   [#permalink] 20 Sep 2017, 15:51
Display posts from previous: Sort by