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# Which of the following could be a value of x, in the diagram above?

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Which of the following could be a value of x, in the diagram above?  [#permalink]

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22 May 2016, 13:43
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Difficulty:

35% (medium)

Question Stats:

72% (01:39) correct 28% (01:27) wrong based on 237 sessions

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Which of the following could be a value of x, in the diagram above?

A. 10
B. 20
C. 40
D. 50
E. any of the above

Attachment:

p002-1.gif [ 988 Bytes | Viewed 15463 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 7981
Re: Which of the following could be a value of x, in the diagram above?  [#permalink]

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22 May 2016, 20:44
4
4
Bunuel wrote:

Which of the following could be a value of x, in the diagram above?

A. 10
B. 20
C. 40
D. 50
E. any of the above

Attachment:
p002-1.gif

Since angle ABC is above angle ADC, angle ABC>angle ADC.... so $$5x>90...... x>\frac{90}{5}........x>18$$
the max value of any angle can be just below 180 but not >180.....so$$5x<180......x<\frac{180}{5}......x<36$$

so $$18<x<36$$

ONLY 20 fits in this range
ans B
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Posts: 4009
Re: Which of the following could be a value of x, in the diagram above?  [#permalink]

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16 Jun 2016, 11:30
Top Contributor
1
Bunuel wrote:

Which of the following could be a value of x, in the diagram above?

A. 10
B. 20
C. 40
D. 50
E. any of the above

Attachment:
p002-1.gif

This question requires us to take note of the fact that there's nothing to suggest that the diagram is not drawn to scale.

IMPORTANT: On the GMAT, the diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.

Since we can assume that the diagram is drawn to scale, we can see that 5x is greater than 90 degrees (and less than 180 degrees). So, the only answer choice that works is B

Here's a video on this topic as well as other assumptions we can make about diagrams on the GMAT

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Joined: 20 Feb 2015
Posts: 762
Concentration: Strategy, General Management
Re: Which of the following could be a value of x, in the diagram above?  [#permalink]

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17 Jun 2016, 01:56
1
Bunuel wrote:

Which of the following could be a value of x, in the diagram above?

A. 10
B. 20
C. 40
D. 50
E. any of the above

Attachment:
p002-1.gif

5x=D+C
or,
5x=90 +C
or,
5x > 90
substituting x = 10 , 5x =50 < 90
now x cannot take values 40 or 50 because that will make 5x > 180
the only option left is 20 , so B
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Joined: 03 Aug 2017
Posts: 64
Re: Which of the following could be a value of x, in the diagram above?  [#permalink]

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04 Apr 2018, 06:04
A. 10
B. 20
C. 40
D. 50
E. any of the above

SOLVING BY ANS CHOICE

A) 10 WHEN X IS 10 5X = 50 AND SINCE 5X IS ON A STRAIGHT LINE 5X +dbc = 180 THERFORE IT MEANS DBC = 180-50 = 130 BUT THAT CANNOT BE AS ONE ANGLE OF THE TRIANGLE IS ALREADY 90 THERFORE A = RULED OUT.

B) X=20 MEans 5x = 100 and angle dbc = 80 therefore 90+80+10 = 180 possible
c) x=40 means 5x= 200 not possible as both angle on a straight line max can be 180
d) x=50 mens 5x=250 not possible as both angle on a straight line = 180 thefore ans = b
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Re: Which of the following could be a value of x, in the diagram above?  [#permalink]

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16 Jun 2019, 12:25
Bunuel wrote:

Which of the following could be a value of x, in the diagram above?

A. 10
B. 20
C. 40
D. 50
E. any of the above

Attachment:
p002-1.gif

Angle B = 180 - 5x

We know that in triangle BDC, angle B is greater than 0 and less than 90 (Since angle D = 90 in triangle BDC)

—> B > 0
—> 180 - 5x > 0
—> 5x < 180
—> x < 36

And B < 90 in triangle BCD
—> 180 - 5x < 90
—> 180 - 90 < 5x
—> 5x > 90
—> x > 18

So 18 < x < 38

Only 1 Option satisfies = 20 degrees

IMO Option B

Pls Hit kudos if you like the solution

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Re: Which of the following could be a value of x, in the diagram above?   [#permalink] 16 Jun 2019, 12:25
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# Which of the following could be a value of x, in the diagram above?

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