NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 07:15 It is currently 25 Apr 2024, 07:15
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

The variables a and b represent the hundreds digits of the two numbers

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92913
Own Kudos [?]: 618949 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
The variables a and b represent the hundreds digits of the two numbers [#permalink] New post   27 Oct 2021, 07:30
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

53% (01:57) correct 47% (02:09) wrong based on 85 sessions
Hide Show timer Statistics
The variables a and b represent the hundreds digits of the two numbers in the inequality \(1a35 < 1b45\). What is the value of 1a35 ?

(1) \(a ≤ b < 2\)

(2) \(2 – (a + b) > 0\)



Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
ShowHide Answer
Official Answer
B
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29925 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: The variables a and b represent the hundreds digits of the two numbers [#permalink] New post   27 Oct 2021, 10:24
Expert Reply
Top Contributor
Bunuel wrote:
The variables a and b represent the hundreds digits of the two numbers in the inequality \(1a35 < 1b45\). What is the value of 1a35 ?

(1) \(a ≤ b < 2\)
(2) \(2 – (a + b) > 0\)

Given: The variables a and b represent the hundreds digits of the two numbers in the inequality 1a35 < 1b45

Target question: What is the value of 1a35 ?

Statement 1: a ≤ b < 2
There are several values of a and b that satisfy statement 1 (and the given information). Here are two:
Case a: a = 0 and b = 0. In this case, the answer to the target question is 1a35 = 1035
Case b: a = 1 and b = 1. In this case, the answer to the target question is 1a35 = 1135
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2 – (a + b) > 0
Add (a + b) to both sides of the inequality to get: 2 > a + b
There are exactly two pairs of values of a and b that satisfy the inequality 2 > a + b (and the given information). They are:
Case a: a = 0 and b = 0. In this case, the answer to the target question is 1a35 = 1035
Case b: a = 0 and b = 1. In this case, the answer to the target question is 1a35 = 1035
Notice that the answer to the target question is the same in both cases: 1a35 = 1035
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

RELATED VIDEO
User avatar
P
sanjitscorps18
Director
Director
Joined: 26 Jan 2019
Posts: 642
Own Kudos [?]: 439 [0]
Given Kudos: 118
Location: India
Schools: Fuqua '24 HKUST Johnson '24 Kellogg '24 LBS '24 Sloan '24 Stanford '24 Wharton '24 Yale '24 Harvard '24
Send PM
Reviews Badge
Re: The variables a and b represent the hundreds digits of the two numbers [#permalink] New post   27 Oct 2021, 10:47
BrentGMATPrepNow wrote:
Bunuel wrote:
The variables a and b represent the hundreds digits of the two numbers in the inequality \(1a35 < 1b45\). What is the value of 1a35 ?

(1) \(a ≤ b < 2\)
(2) \(2 – (a + b) > 0\)

Given: The variables a and b represent the hundreds digits of the two numbers in the inequality 1a35 < 1b45

Target question: What is the value of 1a35 ?

Statement 1: a ≤ b < 2
There are several values of a and b that satisfy statement 1 (and the given information). Here are two:
Case a: a = 0 and b = 0. In this case, the answer to the target question is 1a35 = 1035
Case b: a = 1 and b = 1. In this case, the answer to the target question is 1a35 = 1135
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2 – (a + b) > 0
Add (a + b) to both sides of the inequality to get: 2 > a + b
There are exactly two pairs of values of a and b that satisfy the inequality 2 > a + b (and the given information). They are:
Case a: a = 0 and b = 0. In this case, the answer to the target question is 1a35 = 1035
Case b: a = 0 and b = 1. In this case, the answer to the target question is 1a35 = 1035
Notice that the answer to the target question is the same in both cases: 1a35 = 1035
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

RELATED VIDEO


I believe there would be another case for 2nd statement.

a= 1 and b= 0, since a + b < 2

In that case statement 2 would be insufficient as well.

I am yet to check the statements combined. I will do that edit shortly.

Posted from my mobile device
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29925 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: The variables a and b represent the hundreds digits of the two numbers [#permalink] New post   27 Oct 2021, 10:52
Expert Reply
Top Contributor
sanjitscorps18 wrote:
I believe there would be another case for 2nd statement.

a= 1 and b= 0, since a + b < 2

In that case statement 2 would be insufficient as well.

I am yet to check the statements combined. I will do that edit shortly.

Posted from my mobile device

I almost made the same mistake :-)

While a= 1 and b= 0 satisfies statement 2, those same values don't satisfy the given information: 1a35 < 1b45, since we end up with 1135 < 1045, which is not true
User avatar
P
sanjitscorps18
Director
Director
Joined: 26 Jan 2019
Posts: 642
Own Kudos [?]: 439 [0]
Given Kudos: 118
Location: India
Schools: Fuqua '24 HKUST Johnson '24 Kellogg '24 LBS '24 Sloan '24 Stanford '24 Wharton '24 Yale '24 Harvard '24
Send PM
Reviews Badge
Re: The variables a and b represent the hundreds digits of the two numbers [#permalink] New post   27 Oct 2021, 10:59
BrentGMATPrepNow wrote:
sanjitscorps18 wrote:
I believe there would be another case for 2nd statement.

a= 1 and b= 0, since a + b < 2

In that case statement 2 would be insufficient as well.

I am yet to check the statements combined. I will do that edit shortly.

Posted from my mobile device

I almost made the same mistake :-)

While a= 1 and b= 0 satisfies statement 2, those same values don't satisfy the given information: 1a35 < 1b45, since we end up with 1135 < 1045, which is not true


Yeah, true. I was checking this on my phone and it never works for me. Yes, B should be the correct option then.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92913
Own Kudos [?]: 618949 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: The variables a and b represent the hundreds digits of the two numbers [#permalink] New post   03 Nov 2021, 06:50
Expert Reply
This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32675
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: The variables a and b represent the hundreds digits of the two numbers [#permalink] New post   26 Dec 2022, 12:51
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 Club Bot
gmatclubot
Re: The variables a and b represent the hundreds digits of the two numbers [#permalink]
26 Dec 2022, 12:51
Moderator:
Bunuel
Math Expert
92912 posts

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