Last visit was: 09 Jul 2025, 00:16 It is currently 09 Jul 2025, 00:16
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
555-605 Level|   Algebra|         
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 9 July 2025
Posts: 102,597
Own Kudos:
739,647
 [20]
Given Kudos: 97,452
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,597
Kudos: 739,647
 [20]
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 05 Nov 2015, 12:24
Kudos
Add Kudos
20
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

80% (01:53) correct 20% (02:09) wrong based on 1074 sessions

History

Date
Time
Result
Not Attempted Yet
If \(x = \frac{a}{2} + \frac{b}{2^3} + \frac{c}{2^4}\), where a, b, and c are each equal to 0 or 1, then x could be each of the following EXCEPT


(A) 1/16

(B) 3/16

(C) 5/16

(D) 10/16

(E) 11/16
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Skywalker18
User avatar
Retired Moderator
Joined: 08 Dec 2013
Last visit: 15 Nov 2023
Posts: 2,052
Own Kudos:
9,677
 [5]
Given Kudos: 171
Status:Greatness begins beyond your comfort zone
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Products:
My Reviews
Posts: 2,052
Kudos: 9,677
 [5]
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 05 Nov 2015, 18:57
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
x= a/2 + b/2^3 + c/2^4
= a/2 + b/8 + c/16
= (8a + 2b + c)/16

Depending on whether a, b and c take 0 or 1 , we will have 1,3,10 and 11 as sum in the numerator of the expression .

Answer C
General Discussion
User avatar
camlan1990
User avatar
Joined: 11 Sep 2013
Last visit: 19 Sep 2016
Posts: 96
Own Kudos:
262
Given Kudos: 26
Schools: Kenan-Flagler '17 SMU '17 McCombs '19
Schools: Kenan-Flagler '17 SMU '17 McCombs '19
Posts: 96
Kudos: 262
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 05 Nov 2015, 12:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1, then x could be each of the following EXCEPT

(A) 1/16
(B) 3/16
(C) 5/16
(D) 10/16
(E) 11/16

x = a/2 + b/2^3 + c/2^4 = 8a/16 + 2b/16 + c/16
(A) 1/16 when a=b=0, c=1
(B) 3/16 when a = 0, b=c=1
(D) 10/16 when a=b=1, c=0
(E) 11/16 when a=b=c=1

(C) 5/16 there is no value of a, b, c (0 or 1)

Ans: C
User avatar
asethi
User avatar
Joined: 08 Sep 2015
Last visit: 08 Jan 2016
Posts: 57
Own Kudos:
37
Given Kudos: 6
Status:tough ... ? Naaahhh !!!!
Location: India
Concentration: Marketing, Strategy
WE:Marketing (Computer Hardware)
Posts: 57
Kudos: 37
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 05 Nov 2015, 22:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x cannot be 5/16

Ans:c
avatar
Amidro
avatar
Joined: 02 Oct 2015
Last visit: 13 Mar 2019
Posts: 9
Own Kudos:
15
Given Kudos: 21
Location: Uzbekistan
Concentration: Entrepreneurship, Strategy
GMAT 1: 570 Q39 V29
GPA: 3.9
WE:General Management (Pharmaceuticals and Biotech)
GMAT 1: 570 Q39 V29
Posts: 9
Kudos: 15
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 06 Nov 2015, 00:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nice post, tricky one.
IMO C
A,B,D,E can be easily eliminated as we have 0 or 1 to choose for values of a,b,c respectively.
A ->>> easy to get 1/16 (just setting 0 for a & b)
B - >>> setting 0 for a, now we have 2/16 (which is 1/8 reversed to 2/16) we get 3/16
D ->>> Getting (1/2 with 8/16 and b=1, c=0)
E - >>> a=b=c=1
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 08 Jul 2025
Posts: 11,296
Own Kudos:
41,621
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,296
Kudos: 41,621
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 27 Jan 2018, 09:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(x = \frac{a}{2} + \frac{b}{2^3} + \frac{c}{2^4}\), where a, b, and c are each equal to 0 or 1, then x could be each of the following EXCEPT


(A) 1/16

(B) 3/16

(C) 5/16

(D) 10/16

(E) 11/16


Something that may help you in getting to the answer..
All except D are odd/16, so C/16 =1/16....A
now work on other two to see if they add up to answer..
a/2+b/8+1/16....
a=b=1... 1/2+1/8+1/16=11/16 ...E
a=0 b=1...1/8+1/16 = 3/16...B
a=b=0...1/16...A

Ok now 10/16 is nothing but 5/8..
So c is 0... So 1/2+1/8=5/8...D

Ans C
User avatar
Basshead
User avatar
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 927
Own Kudos:
286
 [1]
Given Kudos: 432
Location: United States
Posts: 927
Kudos: 286
 [1]
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 24 Oct 2020, 14:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If \(x = \frac{a}{2} + \frac{b}{2^3} + \frac{c}{2^4}\), then:

\(\frac{8a}{16} + \frac{2b}{16} + \frac{1c}{16}\)

If a, b, and c are each equal to 0 or 1, there will be on answer that is impossible. Lets look at the choices-

(A) 1/16 -- Possible with C

(B) 3/16 -- Possible with B and C

(C) 5/16 -- Not possible

(D) 10/16 -- Possible with A and B

(E) 11/16 -- Possible with A and B and C

Answer is C.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
18,723
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,723
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 25 Oct 2020, 01:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x = \(\frac{a}{2} + \frac{b}{2^3} + \frac{c}{2^4}\)

=> x = \(\frac{(2^3a + 2b + 1c)}{ 2^4} = \frac{(8a + 2b + c) }{ 16}\)

If a = b = c = 0, Then x = 0.

If a = b = c = 1, Then x = \(\frac{1}{2} + \frac{1}{2^3} + \frac{1}{2^4}\)

=> x = \(\frac{(2^3 + 2 + 1)}{ 2^4} = \frac{11}{ 16}\)

So, \(0 ≤ x ≤ \frac{11}{16}\)

Various values for 8a + 2b + c:

=> All '0' = 0
=> All '1' = 11
=> 8 + 2 = 10 when c = 0
=> 8 + 1 = 9 when b = 0
=> 2 + 1 = 3 when when a = 0

Value not possible is '5'.

Answer C
avatar
Vrishnipradeep
avatar
Joined: 31 Dec 2020
Last visit: 20 Jun 2021
Posts: 1
Given Kudos: 2
Posts: 1
Kudos: 0
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 26 Mar 2021, 12:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Correct me if i am wrong ,
If C=0 i.e as per option D how can the denominator be 16 ,
C / 2^4 = 0 / 2^4 = 0 ,
then the denominator becomes 8.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,360
Own Kudos:
1,010
Posts: 37,360
Kudos: 1,010
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 27 May 2025, 10:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
102597 posts
Krunaal
PS Forum Moderator
679 posts