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

 It is currently 22 Jul 2018, 05:49

### 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

# x, a, z, and b are single digit positive integers. x = ¼ a.

Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 120
x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

12 Mar 2013, 08:36
4
8
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:46) correct 28% (01:54) wrong based on 316 sessions

### HideShow timer Statistics

x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal

A. 33
B. 36
C. 44
D. 63
E. 66

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

12 Mar 2013, 08:51
5
4
emmak wrote:
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal
a) 33
b) 36
c) 44
d) 63
e) 66

Without doing any algebra, you can reason out that the first part of the subtraction will be exactly four times bigger than the second part of the subtraction. Since all of the numbers are integers, it means that a and be will be divisible by 4 (while x and z can be anything). Once you subtract 1/4 from a and b, you'll be left with 3/4 of what they were orignally, which must be divisible by 3. The answer will necessarily be divisible by 3, so it elmininates answer choices a, b, d and e. Answer choice C is the only impossible outcome.

This type of question can lead people down rabbit holes, trying to calculate every possible number, especially with a premise as tempting as "single digit positive integers". There can't be that many choices, right? Doing this the long way may work out well, but you can't beat conceptual understanding for giving you the right answer in the most efficient way.

Hope this helps!
-Ron
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 619
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

12 Mar 2013, 09:16
4
3
emmak wrote:
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal
a) 33
b) 36
c) 44
d) 63
e) 66

(10a+b)-(10x+z) = 10(a-x)+(b-z) = 10(4x-x)+(4z-z) = 3*10(x+z). Thus the sum has to be a multiple of 3.Only option C is not a multiple of 3.

C.
_________________
##### General Discussion
Intern
Joined: 05 Feb 2013
Posts: 1
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

12 Mar 2013, 09:47
1
emmak wrote:
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal
a) 33
b) 36
c) 44
d) 63
e) 66

From the given equations, a = 4x, b = 4z

(10a+b) - (10x+z) = 40x+4z - 10x-z = 30x +3z = 3(10x+z)

Therefore the resultant should be divisible by 3 which isn't possible only in the case of C.

Manager
Joined: 17 Dec 2013
Posts: 58
GMAT Date: 01-08-2015
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

12 Jan 2015, 11:26
1
another way, not as short as the methods mentioned above but also helpfull:

"x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal"

since they are all single digit positive integers, x and z could be 1 or 2, a and b would become 4 or 8.

if you look at the answer choies you can see a pattern in the single digit's. if you evaluate the possibility for the single digit of (10a + b) – (10x + z), you get:

single digit: b-z
if z=1, b=4
if z=2, b=8.

so 4-1=3 or 8-2=6

I hope its understandable
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

13 Jan 2015, 02:03
pranbo wrote:
emmak wrote:
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal
a) 33
b) 36
c) 44
d) 63
e) 66

From the given equations, a = 4x, b = 4z

(10a+b) - (10x+z) = 40x+4z - 10x-z = 30x +3z = 3(10x+z)

Therefore the resultant should be divisible by 3 which isn't possible only in the case of C.

Did in the same way. Just like to add.... instead of 44, if the option had been 48 or some multiple of 3, then again all yielded values would had to be checked
_________________

Kindly press "+1 Kudos" to appreciate

Director
Joined: 23 Jan 2013
Posts: 600
Schools: Cambridge'16
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

04 Feb 2016, 02:20
did by algebra use

a=4x, b=4z

10a+b-10x-z
10(a-x)+b-z, by substitution get 30x+3z => 3(10x+z). So, should be multiple of 3

Only C does not fit
Math Expert
Joined: 02 Aug 2009
Posts: 6277
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

04 Feb 2016, 02:43
1
emmak wrote:
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal

A. 33
B. 36
C. 44
D. 63
E. 66

Hi,
almost everyone has done by considerimg non multiple of 3..
But if it doe snot strike in the stress of the exam, another method would be..

1) firstly we are not given that all are different integers..
2) since each is a positive single digit integer and x=a/4... a can take only 4 and 8 as value, and x can take 1 and 2..
3) same as 2) for b and z.

so in (10a + b) – (10x + z) ..

10a+b can be
44,48,84,88..

10x+z can be
11,12,21,22..

lets see teh choices
A. 33.. 44-11 possible
B. 36..48-12
C. 44.. no combination possible
D. 63..84-21
E. 66..88-22

ans C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Retired Moderator
Joined: 18 Sep 2014
Posts: 1165
Location: India
x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

08 May 2016, 07:20
Original Explanation:

Solution: C

Spot the pattern here.

All four variables must represent integers, so if x = ¼ a and z = ¼ b, then both a and b must be either 4 or 8.

Now try all four possibilities.

If a = 4 and b = 4, then (10a+b) – (10x+z) = 44 – 11 = 33.
If a = 4 and b = 8, then (10a+b) – (10x+z) = 48 – 12 = 36.
If a = 8 and b = 4, then (10a+b) – (10x+z) = 84 – 21 = 63.
If a = 8 and b = 8, then (10a+b) – (10x+z) = 88 – 22 = 66.

(C) is impossible.
_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.

My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
http://gmatclub.com/forum/possessive-pronouns-200496.html
http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773

Non-Human User
Joined: 09 Sep 2013
Posts: 7326
Re: x, a, z, and b are single digit positive integers. x = ¼ a.  [#permalink]

### Show Tags

19 Aug 2017, 16:49
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.
_________________
Re: x, a, z, and b are single digit positive integers. x = ¼ a. &nbs [#permalink] 19 Aug 2017, 16:49
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.