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

 It is currently 26 Jun 2019, 15:38 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree

Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55801
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 84% (00:58) correct 16% (01:12) wrong based on 78 sessions

HideShow timer Statistics In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

_________________
Director  V
Joined: 04 Dec 2015
Posts: 740
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

1
Bunuel wrote:
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

Let $$∠C = x$$

$$∠B = x + 10$$

$$∠A = x + 10 + 10 = x + 20$$

$$∠A + ∠B + ∠C = 180$$

$$x + 20 + x + 10 + x = 180$$

$$3x + 30 = 180$$

$$3x = 180 - 30 = 150$$

$$x = 150/3 = 50$$

$$∠C = 50$$

$$∠B =x + 10 = 50 + 10 = 60$$ . Answer (D) ...
Senior SC Moderator V
Joined: 22 May 2016
Posts: 2950
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

Bunuel wrote:
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

Define all angles in terms of ∠B (= b, ∠A = a, ∠C = c).

Quote:
∠A is 10 degrees greater than ∠B

a = b + 10
Quote:
∠B is 10 degrees greater than ∠C

b = c + 10, or

c = b - 10

a + b + c = 180, substitute values in bold type

(b + 10) + b + (b - 10) = 180

3b = 180

b = 60
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3364
Location: India
GPA: 3.12
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

The sum of all the angles in a triangle is 180 Degree.
If the three angles have to differ by 10 and add to 180,
the only possibility(with a difference of 10) is when the three angles are 50,60 and 70.

Since ∠B is 10 degree greater than ∠C and 10 degree smaller than ∠A, it must be 60(Option D)
_________________
You've got what it takes, but it will take everything you've got
Manager  S
Joined: 05 Nov 2014
Posts: 104
Location: India
Concentration: Strategy, Operations
GMAT 1: 580 Q49 V21 GPA: 3.75
Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

Solution:
Given:
a=b+10
b=c+10
Also, we know
a+b+c=180.----eq (1)

Therfore subsitute the value of a and c in the eq(1)
we ger
b+10+b+b-10=180.
3b=180.
b=60.

So Option D
Math Expert V
Joined: 02 Aug 2009
Posts: 7765
Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

Bunuel wrote:
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

Hi,

Here actually difference of 10 doesn't matter. Any difference but similar would give us SAME answer as 60.. WHY?

The three angles differ by certain amount so they are in AP and central angle B would be the MEAN
So 3*B =180..... B=60
D
_________________
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1437
Location: India
Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

If all three angles are equal: 60, 60, 60

If the three angles are in Arithmetic Progression with a difference of 10: 50, 60, 70

So the central angle is 60 only. Hence D answer
Director  D
Joined: 13 Mar 2017
Posts: 729
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

Bunuel wrote:
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

Let the /_C = x
So, /_ B = x +10
/_ A = x +20

A + B + C = x+20 + x +10 +x = 180
-> 3x +30 = 180
-> x= 150/3 = 50

So, /_B = 50 +10 = 60

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Board of Directors P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4505
Location: India
GPA: 3.5
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

Bunuel wrote:
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

Let the value of $$∠A = a°$$ , $$∠B = b°$$ and $$∠C = c°$$

We know, $$∠A + ∠B + ∠C = 180°$$ Or, $$a° + b° + c° = 180°$$
Quote:
∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C

Value of $$∠B$$ = $$( c° + 10° )$$
Value of $$∠A$$ = $$( b° + 10° )$$ => $$( c° + 10° ) + 10°$$ = $$c° + 20°$$
Value of $$∠C$$ = c°

Now, $$(c° + 20°)$$ + $$( c° + 10° )$$ + $$c°$$ = $$180°$$

Or, $$3c° + 30° = 180°$$

Or, $$3c° = 150°$$

So, c° = 50°

Now, as Value of $$∠B$$ = $$( c° + 10° )$$ = $$60°$$

Thus, answer will be (D) 60°
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

Bunuel wrote:
In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degrees greater than ∠C. The value of angle B is

(A) 30
(B) 40
(C) 50
(D) 60
(E) 70

We can let angle C = x, angle B = 10 + x, and angle A = 20 + x. Since there are 180 degrees in a triangle, we have:

x + x + 10 + x + 20 = 180

3x + 30 = 180

3x = 150

x = 50

Thus, angle B is 50 + 10 = 60 degrees.

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP  D
Status: Learning
Joined: 20 Dec 2015
Posts: 1006
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36 GRE 1: Q157 V157 GPA: 3.4
WE: Engineering (Manufacturing)
Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

IMO D
A+B+C=180
B+10+B+B-10=180
3B=180
B=60
_________________
Intern  B
Joined: 11 Mar 2015
Posts: 32
Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  [#permalink]

Show Tags

Here,<A+<B+<C=180 and B=C+10, A=B+10=>A=C+10+10 =>A=C+20
Hence, C+20+C+10+C=180
C=150/3=50 Re: In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree   [#permalink] 16 Dec 2017, 03:21
Display posts from previous: Sort by

In Triangle ABC, ∠A is 10 degrees greater than ∠B, and ∠B is 10 degree  