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

 It is currently 22 Feb 2019, 07:01

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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

If a and b are two-digit numbers that share the same digits, but in re

Author Message
TAGS:

Hide Tags

Intern
Joined: 31 Jan 2018
Posts: 9
If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

03 Feb 2018, 21:26
2
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:16) correct 39% (02:13) wrong based on 134 sessions

HideShow timer Statistics

If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

03 Feb 2018, 21:56
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

Let a be xy that is 10x+y and b will be 10y+x..
1) a-b=10x+y-10y-x=9(x-y)=45..... x-y=5..
Number a could be 61,72,83 or 94
Insuff
2) a is MULTIPLE of 9
Number could be 81,72,54 etc
Insufficient

Combined ..
Only 72 fits in both cases..
Sufficient

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Math Expert
Joined: 02 Sep 2009
Posts: 53069
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

03 Feb 2018, 22:56
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

Similar question to practice: https://gmatclub.com/forum/if-a-and-b-a ... 94795.html
_________________
Retired Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

03 Feb 2018, 23:07
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

Let $$a=10x+y$$ and $$b=10y+x$$, where $$x$$ & $$y$$ are digits of the two digit number $$a$$ & $$b$$. To know the value of $$a$$ we need the value of $$x$$ & $$y$$

Statement 1: $$a-b=10x+y-10y-x=45$$

$$=>9(x-y)=45=>x-y=5$$. Two variable one equation. Insufficient

Statement 2: $$a$$ is multiple of $$9$$, hence sum of digits must be multiple of $$9$$

$$=> x+y=9$$ or $$x+y=18$$. Again two variable, one equation. Insufficient

Combining 1 & 2: $$x-y=5$$ & $$x+y=9$$, solving we get $$x=7$$ & $$y=2$$

for $$x+y=18$$, we will not get $$x$$ as integer, hence $$x+y=18$$ is not possible.

Therefore $$a=72$$. Sufficient

Option C
Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

09 Feb 2018, 06:54
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

Let a = xy, b = yx

Statement I:

$$a - b = 45,$$
$$x - y = 5$$. The values of $$(x,y) = (6,1) (7,2) (8,3) (9,4)$$.. Insufficient.

Statement II:

Not sufficient as the numbers can be $$18, 27, 36,45, 54, 63....$$

Combine I & II:

$$(x,y) = (7,2)$$... Sufficient.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Intern
Joined: 29 May 2018
Posts: 1
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

03 Jan 2019, 11:45
Was it mentioned that both numbers should be positive?
why cant a be -27?
a=-27 and b=-72
a-b=45
a is a multiple of 9

i chose E thinking on this line.
what am i doing wrong?
Re: If a and b are two-digit numbers that share the same digits, but in re   [#permalink] 03 Jan 2019, 11:45
Display posts from previous: Sort by