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# What is the measure of angle JOM in the figure above?

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Math Expert
Joined: 02 Sep 2009
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What is the measure of angle JOM in the figure above?  [#permalink]

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24 Aug 2018, 05:22
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Difficulty:

15% (low)

Question Stats:

94% (00:59) correct 6% (01:05) wrong based on 39 sessions

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What is the measure of angle JOM in the figure above?

(1) The measure of angle JOL is 48°.
(2) Angle JOK is two-thirds of angle KOL and angle KOL is one-half of angle LOM.

Attachment:

image005.jpg [ 4.05 KiB | Viewed 618 times ]

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What is the measure of angle JOM in the figure above?  [#permalink]

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24 Aug 2018, 05:33
From 1: No idea about other angles.
Hence insufficient.

From 2: JOK = 2/3KOL
KOL = 1/2LOM

JOM = JOK+KOL+LOM = 2/3KOL+KOL+2KOL.
Since we don't know KOL. 2 is also insufficient.

Combining both gives us the answer.

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Re: What is the measure of angle JOM in the figure above?  [#permalink]

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24 Aug 2018, 05:39
Bunuel wrote:

What is the measure of angle JOM in the figure above?

(1) The measure of angle JOL is 48°.
(2) Angle JOK is two-thirds of angle KOL and angle KOL is one-half of angle LOM.

Attachment:
image005.jpg

Angle JOM is the sum of all its sub-angles.
a) Relationship between sub-angles and'
b) measure of any of the angles is required.

St1:-The measure of angle JOL is 48°.
Note(a) absent.
Insufficient.

St2:- Angle JOK is two-thirds of angle KOL and angle KOL is one-half of angle LOM.
Note(b) absent.
Insufficient.

Combines, both the required info available.
Sufficient.

Ans.(C)
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What is the measure of angle JOM in the figure above?  [#permalink]

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24 Aug 2018, 10:43
Statement 1 is insufficient as it gives only measurement of JOL
Statement 2 JOK=2/3KOL, KOL=1/2LOM, no measurement is given hence insufficient

Combining 1 and 2
We get each angle hence sufficient, no need to waste time on finding exact value.

Ans C
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What is the measure of angle JOM in the figure above?  [#permalink]

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24 Aug 2018, 10:50

Solution

Given:
• We are given a figure

To find:
• The measure of angle JOM

Analysing Statement 1
• We are given ∠JOL = 48 degrees
• From this, we can only infer that ∠JOM > 48 degrees, since ∠JOM = ∠JOL + ∠LOM
Therefore, Statement 1 alone is not sufficient to answer this question

Analysing Statement 2
• ∠JOK = 2/3 * ∠KOL
• ∠KOL = 1/2 * ∠LOM
• We cannot find the value of any angle, with this information
Therefore, Statement 2 alone is not sufficient to answer this question.

Combining Both Statements
• Combining both the statements, we get
o ∠JOK + ∠KOL = 48 degrees, since ∠JOL = ∠JOK + ∠KOL ……. (1)
o And we know, ∠JOK = 2/3 * ∠KOL
o Substituting this in (1), we get the value of ∠KOL
o This gives, the value of ∠LOM, since ∠KOL = ½ * ∠LOM
o Therefore, we can find the value of ∠JOM, which is equal to 48 + ∠LOM
Thus, Statement (1) and (2) TOGETHER are sufficient to answer the question

Hence, the correct answer is option C.

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What is the measure of angle JOM in the figure above?   [#permalink] 24 Aug 2018, 10:50
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