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

It is currently 14 Nov 2019, 19:27

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If X = a/2^2 + b/2^3 + c/2^5, does X = 5/16 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59039
If X = a/2^2 + b/2^3 + c/2^5, does X = 5/16 ?  [#permalink]

Show Tags

New post 18 Oct 2019, 03:14
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

31% (02:14) correct 69% (01:57) wrong based on 54 sessions

HideShow timer Statistics

SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1839
Location: India
Premium Member Reviews Badge CAT Tests
If X = a/2^2 + b/2^3 + c/2^5, does X = 5/16 ?  [#permalink]

Show Tags

New post Updated on: 20 Oct 2019, 06:27
Bunuel wrote:
If \(X = \frac{a}{2^2} + \frac{b}{2^3} + \frac{c}{2^5}\), does X = 5/16 ?

(1) a, b, and c are each either 0 or 1.

(2) The greatest possible value of X is 13/32.


Asked: If \(X = \frac{a}{2^2} + \frac{b}{2^3} + \frac{c}{2^5}\), does X = 5/16 ?

(1) a, b, and c are each either 0 or 1.
X = (8a + 4b + c)/32 = 10/32
It is not possible to arrive at (8a + 4b + c) = 10 if a, b & c are either 0 or 1.
SUFFICIENT

(2) The greatest possible value of X is 13/32.
X = a/4 + b/8 + c/32 = (8a + 4b + c)/32
max(8a+4b+c) = 13
Since values of 8a+4b+c is unknown
NOT SUFFICIENT

IMO A
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com

Originally posted by Kinshook on 18 Oct 2019, 04:26.
Last edited by Kinshook on 20 Oct 2019, 06:27, edited 2 times in total.
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1061
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If X = a/2^2 + b/2^3 + c/2^5, does X = 5/16 ?  [#permalink]

Show Tags

New post 18 Oct 2019, 19:35
Bunuel wrote:
If \(X = \frac{a}{2^2} + \frac{b}{2^3} + \frac{c}{2^5}\), does X = 5/16 ?


(1) a, b, and c are each either 0 or 1.

(2) The greatest possible value of X is 13/32.


Is x = 5/16 or 10/32

\(X = \frac{a}{2^2} + \frac{b}{2^3} + \frac{c}{2^5}\)
—> \(X = \frac{(8a + 4b + c)}{32}\)

(1) a, b, and c are each either 0 or 1.

When a, b, c takes either 0 or 1, we can see the numerator can never take the value 10

Possible values of
(a, b, c) = (0, 0, 0) —> X = 0/32
(a, b, c) = (0, 0, 1) —> X = 1/32
(a, b, c) = (0, 1, 0) —> X = 4/32
(a, b, c) = (1, 0, 0) —> X = 8/32
(a, b, c) = (0, 1, 1) —> X = 5/32
(a, b, c) = (1, 1, 0) —> X = 12/32
(a, b, c) = (1, 0, 1) —> X = 9/32
(a, b, c) = (1, 1, 1) —> X = 13/32

—> A definite no. X can never be 10/32
—> Sufficient

(2) The greatest possible value of X is 13/32
—> 8a + 4b + c = 13

We can adjust values of a, b & c to get the greatest value as 13 and one of the values as 10

Case 1: As per statement (1) maximum value is 13/32 and X is never equal to 10/32

Case 2: Let the Maximum values of a, b and c can be 1
—> Maximum value of X = (8+4+1)/32 = 13/32
We can also assume one possible set of values, a = 1, b = 1/2, c = 0
—> X = (8*1 + 4*1/2 + 0)/32 = 10/32

So, we get 2 outcomes —> Insufficient

IMO Option A

Posted from my mobile device
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8165
Re: If X = a/2^2 + b/2^3 + c/2^5, does X = 5/16 ?  [#permalink]

Show Tags

New post 18 Oct 2019, 20:04
Bunuel wrote:
If \(X = \frac{a}{2^2} + \frac{b}{2^3} + \frac{c}{2^5}\), does X = 5/16 ?


(1) a, b, and c are each either 0 or 1.

(2) The greatest possible value of X is 13/32.



\(X = \frac{a}{2^2} + \frac{b}{2^3} + \frac{c}{2^5} = \frac{a}{4} + \frac{b}{8} + \frac{c}{32}=\frac{8a+4b+c}{32}\)

So we have to find if \(\frac{8a+4b+c}{32}=\frac{5}{16}=\frac{10}{32}\) or is \(8a+4b+c=10\)

(1) a, b, and c are each either 0 or 1.
Is \(8a+4b+c=10\)? c has to be even for that as all other terms 8a, 4b and 10 are even, so ONLY possible value is 0.
So, is 8a+4b=10... if you fill a and b as 0 or 1, the values of 8a+4b you will get is 0, 4, 8, 12.
Hence, answer is NO
Suff

(2) The greatest possible value of X is 13/32.
So, \(8a+4b+c=13\)..
When a=b=c=1, \(8a+4b+c=13\)
When a=0, b=3, and a=1, \(8a+4b+c=10\)
But, we can also have a=b=1, c=0, then 12/32, so there can be various possibilities from 0/32 to 13/32
Insuff

A
_________________
GMAT Club Bot
Re: If X = a/2^2 + b/2^3 + c/2^5, does X = 5/16 ?   [#permalink] 18 Oct 2019, 20:04
Display posts from previous: Sort by

If X = a/2^2 + b/2^3 + c/2^5, does X = 5/16 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne