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

It is currently 16 Dec 2019, 01:31

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

Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59749
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 20 Oct 2019, 21:48
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

49% (01:32) correct 51% (01:58) wrong based on 43 sessions

HideShow timer Statistics

Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8331
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 20 Oct 2019, 22:02
1
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
So \(O\geq{5}\), as ∆.O∆ becomes O when rounded to nearest integer. Also ∆+1=O, as ∆ converts to O.
But the decimal could be 4.54 or 5.65 or 6.76 or 7.87 or 8.98.. so the value of ∆ could be in the range \(4\leq{∆}\leq{8}\)

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
This tells us that ∆<5 as the tenth digit does not change, so range becomes \(0\leq{∆}\leq{4}\)

Combined..
∆ will be 4, and the number is 4.54

C
_________________
Director
Director
avatar
P
Joined: 18 May 2019
Posts: 557
GMAT ToolKit User Premium Member CAT Tests
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post Updated on: 20 Oct 2019, 22:26
1
Given ∆.O∆, where ∆ and O are distinct digits. We are to determine ∆.

From statement 1, rounding ∆.O∆ to the nearest integer yields O
For this to occur, we know O must have the following possible values: 5,6,7,8,9
while ∆ can be any of the following: 4,5,6,7,8,9
There are many possibilities for ∆ hence statement 1 is not sufficient on its own.

From Statement 2, rounding ∆.O∆ to the nearest tenth decimal yields ∆.O
this implies ∆ is less than 5. hence ∆ can be 1,2,3,4
Statement 2 is not sufficient.

1+2
means ∆ = 4. This is because 4 is the only common possible value in both statements.
Both statements taken together are sufficient to answer the question.

The answer is therefore C.

Originally posted by eakabuah on 20 Oct 2019, 22:25.
Last edited by eakabuah on 20 Oct 2019, 22:26, edited 1 time in total.
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 1886
Location: India
Premium Member Reviews Badge CAT Tests
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 20 Oct 2019, 22:26
1
Given: Let ∆ and O be two distinct digits in the decimal ∆.O∆

Asked: what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
O = ∆ + 1
∆ >= 4
∆ = {4,5,6,7,8}
There may be many such pairs
NOT SUFFICIENT

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
∆ < 5
∆ = {0,1,2,3,4}
NOT SUFFICIENT

(1) + (2)
(1) When rounded to the nearest integer, the decimal becomes O
O = ∆ + 1
∆ = {4,5,6,7,8}
(2) When rounded to the nearest tenth, the decimal becomes ∆.O
∆ < 5
∆ = {0,1,2,3,4}
∆ = 4
Only 4.54 satisfy both conditions
SUFFICIENT

IMO C
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 342
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 20 Oct 2019, 22:45
1
(1) When rounded to the nearest integer, the decimal becomes O
Then values of ∆ and O will be.... ∆= O-1where O=5,6,7,8,9 and ∆= 4,5,6,7,8.....So insufficient


(2) When rounded to the nearest tenth, the decimal becomes ∆.O

Then ∆ =0,1,2,3,4.....So insufficient



From both we can get ∆=4 , O=5

4.54


OA:C

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 05 Aug 2018
Posts: 72
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 20 Oct 2019, 22:52
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
Rounded to nearest integer, the decimal should be .0
Therefore, O = 0
However, we do not know anything about ∆ - INSUFFICIENT

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
Rounded to nearest integer, the decimal becomes as above, we can infer that ∆ is between 0 - 4, but we dont know which number. - INSUFFICIENT

Taken (1) + (2) together, insufficient because we do not know ∆

Thus, E is the correct answer choice.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5485
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post Updated on: 22 Oct 2019, 02:52
given ∆.O∆
find value of ∆
#1
When rounded to the nearest integer, the decimal becomes O
it means that ∆ is 1,2,3,4
insufficient
#2

When rounded to the nearest tenth, the decimal becomes ∆.O
∆ can be 1,2,3,4 and O can be any integer value 0-9 insufficeint
from 1&2
∆=4 and O = 5
4.54
sufficient IMO C

Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
(2) When rounded to the nearest tenth, the decimal becomes ∆.O

Originally posted by Archit3110 on 21 Oct 2019, 01:59.
Last edited by Archit3110 on 22 Oct 2019, 02:52, edited 1 time in total.
Senior Manager
Senior Manager
avatar
P
Joined: 25 Jul 2018
Posts: 403
CAT Tests
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 21 Oct 2019, 04:48
1
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(Statement1): When rounded to the nearest integer, the decimal becomes O
∆.O∆- could be:
--> 4.54≈5
--> 5.65≈6
--> 6.76≈7
...
----------
4≤ ∆≤8

Insufficient

(Statement2): When rounded to the nearest tenth, the decimal becomes ∆.O
--> 2.52 ≈2.5
--> 3.43 ≈3.4
--> 4.54 ≈4.5
...
--------------
1≤ ∆≤ 4
Insufficient

Taken together 1&2,
Only ∆=4 satisfies the both statements

--> 4.54 ≈5 (statement1)
--> 4.54 ≈4.5 (statement2)

Sufficient

The answer is C
Manager
Manager
User avatar
G
Joined: 17 Jan 2019
Posts: 127
GMAT ToolKit User Premium Member Reviews Badge
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 21 Oct 2019, 05:46
1
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
meaning, ∆=O-1 and O> or =5
∆ can be 4,5,6,7,8
insufficient

(2) When rounded to the nearest tenth, the decimal becomes ∆.O
∆ can be 0,1,2,3,4
insufficient

Together, ∆ must be 4
Therefore, C
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 973
Location: United States
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 21 Oct 2019, 07:13
1
Quote:
Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

(1) When rounded to the nearest integer, the decimal becomes O
(2) When rounded to the nearest tenth, the decimal becomes ∆.O


∆ and O are two DISTINCT digits

(1) When rounded to the nearest integer, the decimal becomes O insufic.

round.integer(∆.O∆)=O; so O=∆+1≥5
if ∆.O∆=4.54 rounded=5; (O,∆)=(5,4)
if ∆.O∆=5.65 rounded=5; (O,∆)=(6,5)

(2) When rounded to the nearest tenth, the decimal becomes ∆.O insufic.

round.tenth(∆.O∆)=∆.O; so ∆≤4={0,1,2,3,4}

(1 & 2) sufic.

O=∆+1≥5…∆+1≥5…∆≥4 and ∆≤4…∆=4…O=5

Answer (C)
Intern
Intern
avatar
B
Joined: 02 Mar 2016
Posts: 8
Location: India
Concentration: Finance, Technology
GPA: 3.66
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?  [#permalink]

Show Tags

New post 21 Oct 2019, 12:54
1
While rounding number increases if digit after decimal is greater than equal to 5 i.e., 5,6,7,8,9 else it will be same i.e., for 0 1,2,3,4

Now to question
1) When rounded to the nearest integer, the decimal becomes O
0 can have value 5,6,7,8,9 but at the same time ∆ has to be 4,5,6,7,8.
Therefore not sufficient

2) When rounded to the nearest tenth, the decimal becomes ∆.O
Implies that ∆ has to be less than 5 {0,1,2,3,4} Therefore not sufficient

Combining 1 and 2
∆ = 4

Posted from my mobile device
GMAT Club Bot
Re: Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?   [#permalink] 21 Oct 2019, 12:54
Display posts from previous: Sort by

Let ∆ and O be two distinct digits in the decimal ∆.O∆, what is ∆?

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





cron

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