GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 25 May 2022, 15:50
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1
10 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 86323
CAT Tests Top Member of the Month
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  05 Nov 2015, 11:24
5
Bookmarks
Expert Reply
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

78% (01:52) correct 22% (02:00) wrong based on 501 sessions

Hide Show timer Statistics

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
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
avatar
camlan1990
Manager
Manager
Joined: 11 Sep 2013
Posts: 100
Schools: Kenan-Flagler '17, SMU '17, McCombs '19
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  05 Nov 2015, 11:59
Bunuel wrote:
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
V
Skywalker18
Verbal Forum Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2233
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
GMAT ToolKit User Reviews Badge
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  05 Nov 2015, 17:57
1
Kudos
2
Bookmarks
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
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Signature Read More
avatar
asethi
Manager
Manager
Joined: 07 Sep 2015
Status:tough ... ? Naaahhh !!!!
Posts: 59
Location: India
Concentration: Marketing, Strategy
WE:Marketing (Computer Hardware)
GMAT ToolKit User
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  05 Nov 2015, 21:54
x cannot be 5/16

Ans:c
avatar
Amidro
Intern
Intern
Joined: 02 Oct 2015
Posts: 9
Location: Uzbekistan
Concentration: Entrepreneurship, Strategy
GMAT 1: 570 Q39 V29
GPA: 3.9
WE:General Management (Pharmaceuticals and Biotech)
GMAT ToolKit User
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  05 Nov 2015, 23:43
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
avatar
V
chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 10504
Reviews Badge Top Member of the Month
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  27 Jan 2018, 08:29
Expert Reply
Bunuel wrote:
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
_________________
1. Absolute modulus:. 2. Fractions: 3. Percentage increase: 4. Combinations:
Signature Read More
User avatar
P
Basshead
VP
VP
Joined: 09 Jan 2020
Posts: 1129
Location: United States
If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  24 Oct 2020, 13:35
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.
_________________
Help me get better -- please critique my responses!
Signature Read More
User avatar
V
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 11855
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  25 Oct 2020, 00:45
Expert Reply
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
_________________
MathRevolution: The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] On-demand trial course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting at $79 for on-demand and $60 for tutoring per hour
Signature Read More
avatar
B
Vrishnipradeep
Intern
Intern
Joined: 31 Dec 2020
Posts: 1
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  26 Mar 2021, 11:14
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
Non-Human User
Joined: 09 Sep 2013
Posts: 23099
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink] New post  30 Apr 2022, 10:16
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.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: If x = a/2 + b/2^3 + c/2^4, where a, b, and c are each equal to 0 or 1 [#permalink]
30 Apr 2022, 10:16
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
10504 posts
Bunuel
Math Expert
86323 posts
generis
Senior SC Moderator
5424 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2892 posts

cron

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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions