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

It is currently 24 Sep 2018, 18:26

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

x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
B
Joined: 14 Feb 2018
Posts: 2
x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post Updated on: 20 May 2018, 04:32
5
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (02:36) correct 60% (02:23) wrong based on 101 sessions

HideShow timer Statistics

x = ab.cd, where a, b, c and d are the tens, units, tenths and hundredths digits respectively in the decimal representation of x. If the number obtained when x is rounded to the nearest integer is subtracted from the number 10a + b + 1, what is the result?

(1) 10a + b and 10c + d are prime numbers less than 50

(2) When the number 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1

Originally posted by kratigupta on 19 May 2018, 11:36.
Last edited by gmatbusters on 20 May 2018, 04:32, edited 2 times in total.
Edited a typo.
Manager
Manager
avatar
G
Joined: 01 Aug 2017
Posts: 192
Location: India
Concentration: General Management, Leadership
Schools: ISB '20 (S), IIMA (S)
GMAT 1: 500 Q47 V15
GPA: 3.4
WE: Information Technology (Computer Software)
Premium Member Reviews Badge CAT Tests
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 19 May 2018, 12:13
1
1
kratigupta wrote:
x = ab.cd, where a, b, c and d are the tens, units, tenths and hundredths digits respectively in the decimal representation of x. If the number obtained when x is rounded to the nearest integer is subtracted from the number 10a + b + 1, what is the result?

(1) 10a + b and 10c + d are prime numbers less than 50

(2) When the number 10b+a+d10+c100 is rounded to the nearest integer, the result is 10b +a +1


x can be represented as \(10a+b+\frac{c}{10}+\frac{d}{100}\).

Statement 1 - 10a + b and 10c + d are prime numbers less than 50.

It means that cd < 50. In terms of decimal .cd is less than 0.5.

Hence the number will not be adjusted to next integer. It will remain same 10a+b. Difference can be found. Sufficient.


Statement 2 - When the number 10b+a+d10+c100 is rounded to the nearest integer, the result is 10b +a +1.

100c+10(b+d)+a is rounded. the result is 10b + a +1.

I think there is typo in this. Could you please check it again.
_________________

If it helps you please press Kudos!

Thank You
Sudhanshu

Intern
Intern
avatar
B
Joined: 04 Mar 2018
Posts: 15
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 20 May 2018, 00:31
1
Statement 1 correct.

Two digit Prime number (since 10a +b and 10c_d will be 2-digit) less than 50 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

from the given number c can have value either 1, 2, 3, 4.
so ab.cd is of the form ab.(1/2/3/4)d which when rounded off becomes ab only which is equal to 10a+b.
so when subtracted from 10a+b+1 answer will always be 1.
DS Forum Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 732
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 20 May 2018, 04:38
2
1
x=100a+10b+c/10+d/100
Now after rounding off x can be 100a+10b or 100a+10b+1 depending on the value of c . So the question reduces to is c > or =5

(1) 10a + b and 10c + d are prime numbers less than 50
Since 10c+d<50. hence c <5.
SUFFICIENT.

(2) When the number 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1
Since after rounding off 10b+a+d/10+c/10, we get 10b+a+1, it means d> or =5.
but value of c can not be determined. It can either be < or > or = 5.
So NOT SUFFICIENT.

Answer A
_________________

Win GMAT CLUB Tests - Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

DS Forum Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 732
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 20 May 2018, 05:21
Please note that there is no need to find all the prime numbers less than 50, since 10c+d< 50, we get c<0
Finding prime numbers will eat a lot of precious time in exam.



nightvision wrote:
Statement 1 correct.

Two digit Prime number (since 10a +b and 10c_d will be 2-digit) less than 50 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

from the given number c can have value either 1, 2, 3, 4.
so ab.cd is of the form ab.(1/2/3/4)d which when rounded off becomes ab only which is equal to 10a+b.
so when subtracted from 10a+b+1 answer will always be 1.

_________________

Win GMAT CLUB Tests - Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Intern
Intern
avatar
B
Joined: 12 Sep 2017
Posts: 28
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 28 May 2018, 06:44
gmatbusters wrote:
x=100a+10b+c/10+d/100
Now after rounding off x can be 100a+10b or 100a+10b+1 depending on the value of c . So the question reduces to is c > or =5

(1) 10a + b and 10c + d are prime numbers less than 50
Since 10c+d<50. hence c <5.
SUFFICIENT.

(2) When the number 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1
Since after rounding off 10b+a+d/10+c/10, we get 10b+a+1, it means d> or =5.
but value of c can not be determined. It can either be < or > or = 5.
So NOT SUFFICIENT.

Answer A



Hi

Regarding statement 2, if we get 10b + a + 1 , doesn't that mean the number is rounded up and the number can be rounded up only when c is greater than/ equal to 5 ?
DS Forum Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 732
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 28 May 2018, 06:52
Hi @s
in the question stem x = ab.cd

But as per the statement 2:
(2) When the number 10b+a+d/10+c/100 (Number is ba.dc) is rounded to the nearest integer, the result is 10b +a +1
Since after rounding off 10b+a+d/10+c/10, we get 10b+a+1, it means d> or =5.
but value of c can not be determined. It can either be < or > or = 5.
So NOT SUFFICIENT.

It seems you have considered the number as ba.cd.

I hope it is clear now, Please tag me if you have any further query.

@s wrote:
gmatbusters wrote:
x=100a+10b+c/10+d/100
Now after rounding off x can be 100a+10b or 100a+10b+1 depending on the value of c . So the question reduces to is c > or =5

(1) 10a + b and 10c + d are prime numbers less than 50
Since 10c+d<50. hence c <5.
SUFFICIENT.

(2) When the number 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1
Since after rounding off 10b+a+d/10+c/10, we get 10b+a+1, it means d> or =5.
but value of c can not be determined. It can either be < or > or = 5.
So NOT SUFFICIENT.

Answer A



Hi

Regarding statement 2, if we get 10b + a + 1 , doesn't that mean the number is rounded up and the number can be rounded up only when c is greater than/ equal to 5 ?

_________________

Win GMAT CLUB Tests - Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Intern
Intern
avatar
B
Joined: 12 Sep 2017
Posts: 28
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 28 May 2018, 10:36
gmatbusters wrote:
Hi @s
in the question stem x = ab.cd

But as per the statement 2:
(2) When the number 10b+a+d/10+c/100 (Number is ba.dc) is rounded to the nearest integer, the result is 10b +a +1
Since after rounding off 10b+a+d/10+c/10, we get 10b+a+1, it means d> or =5.
but value of c can not be determined. It can either be < or > or = 5.
So NOT SUFFICIENT.

It seems you have considered the number as ba.cd.

I hope it is clear now, Please tag me if you have any further query.

@s wrote:
gmatbusters wrote:
x=100a+10b+c/10+d/100
Now after rounding off x can be 100a+10b or 100a+10b+1 depending on the value of c . So the question reduces to is c > or =5

(1) 10a + b and 10c + d are prime numbers less than 50
Since 10c+d<50. hence c <5.
SUFFICIENT.

(2) When the number 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1
Since after rounding off 10b+a+d/10+c/10, we get 10b+a+1, it means d> or =5.
but value of c can not be determined. It can either be < or > or = 5.
So NOT SUFFICIENT.

Answer A



Hi

Regarding statement 2, if we get 10b + a + 1 , doesn't that mean the number is rounded up and the number can be rounded up only when c is greater than/ equal to 5 ?



Got it now :) thank you.
Director
Director
avatar
P
Joined: 02 Oct 2017
Posts: 616
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 11 Jun 2018, 08:54
(1) 10a + b and 10c + d are prime numbers less than 50

Means CD<50
So not incremented so
10a+b+1-(10a+b)= 1
Sufficient

(2) When the number 10b+a+d/10+c/100 is rounded to the nearest integer, the result is 10b +a +1

C+d >0.50
But we don't know whether c is greater or d is greater

C is greater than value get incremented
D is greater than value does not get incremented
So multiple cases exist
Insufficient

A is answer

Give kudos if it helps

Posted from my mobile device
Intern
Intern
avatar
Joined: 03 Mar 2014
Posts: 2
x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 26 Jun 2018, 18:47
nightvision wrote:
Statement 1 correct.

Two digit Prime number (since 10a +b and 10c_d will be 2-digit) less than 50 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

from the given number c can have value either 1, 2, 3, 4.
so ab.cd is of the form ab.(1/2/3/4)d which when rounded off becomes ab only which is equal to 10a+b.
so when subtracted from 10a+b+1 answer will always be 1.


If cd = .47, then d will make c as 5 i.e. ab.47 = ab.5 --> 10a + b + 1
But if If cd = .41, then we have ab.41 = ab --> 10a + b
Hence statement 1 is insufficient.

Please correct me if I am wrong.
DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1343
Location: India
Premium Member
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 26 Jun 2018, 22:26
1
Hitman47 wrote:
nightvision wrote:
Statement 1 correct.

Two digit Prime number (since 10a +b and 10c_d will be 2-digit) less than 50 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

from the given number c can have value either 1, 2, 3, 4.
so ab.cd is of the form ab.(1/2/3/4)d which when rounded off becomes ab only which is equal to 10a+b.
so when subtracted from 10a+b+1 answer will always be 1.


If cd = .47, then d will make c as 5 i.e. ab.47 = ab.5 --> 10a + b + 1
But if If cd = .41, then we have ab.41 = ab --> 10a + b
Hence statement 1 is insufficient.

Please correct me if I am wrong.


Hello

If ab.cd= ab.47, then to round off to the nearest integer, we will just look at the value of c (and not consider the value of d).
So here we see that c=4, so we will remove 47 after decimal and just write ab.

(we dont have to change the value of c by looking at the value of d first, thats the rule of rounding off numbers)
Intern
Intern
avatar
Joined: 03 Mar 2014
Posts: 2
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred  [#permalink]

Show Tags

New post 27 Jun 2018, 06:31
amanvermagmat wrote:
Hitman47 wrote:
nightvision wrote:
Statement 1 correct.

Two digit Prime number (since 10a +b and 10c_d will be 2-digit) less than 50 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

from the given number c can have value either 1, 2, 3, 4.
so ab.cd is of the form ab.(1/2/3/4)d which when rounded off becomes ab only which is equal to 10a+b.
so when subtracted from 10a+b+1 answer will always be 1.


If cd = .47, then d will make c as 5 i.e. ab.47 = ab.5 --> 10a + b + 1
But if If cd = .41, then we have ab.41 = ab --> 10a + b
Hence statement 1 is insufficient.

Please correct me if I am wrong.


Hello

If ab.cd= ab.47, then to round off to the nearest integer, we will just look at the value of c (and not consider the value of d).
So here we see that c=4, so we will remove 47 after decimal and just write ab.

(we dont have to change the value of c by looking at the value of d first, thats the rule of rounding off numbers)

I got it. Thanks a lot!
GMAT Club Bot
Re: x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred &nbs [#permalink] 27 Jun 2018, 06:31
Display posts from previous: Sort by

x = ab.cd, where a, b, c and d are the tens, units, tenths and hundred

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

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.