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# In the triangle above, is OQ > 10? (1) OP = 6 (2) PQ = 7

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
In the triangle above, is OQ > 10? (1) OP = 6 (2) PQ = 7  [#permalink]

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09 Sep 2018, 06:59
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:51) correct 31% (00:59) wrong based on 65 sessions

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In the triangle above, is OQ > 10?

(1) OP = 6
(2) PQ = 7

Attachment:

image014.gif [ 1.3 KiB | Viewed 611 times ]

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Re: In the triangle above, is OQ > 10? (1) OP = 6 (2) PQ = 7  [#permalink]

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09 Sep 2018, 07:11
Bunuel wrote:

In the triangle above, is OQ > 10?

(1) OP = 6
(2) PQ = 7

Attachment:
image014.gif

The property we use here is that the sum of any two sides of a triangle should be less than the third side.
(1)
If OP = 6 and PQ = 7, OQ < 13. (Means greater than 10 or less than 10, we don't know)
If OP = 6 and PQ = 4, OQ < 10.
INSUFFICIENT.

(2)
If PQ = 7 and OP = 6, OQ < 13. (Means greater than 10 or less than 10, we don't know)
If PQ = 7 and OP = 3, OQ < 10.
INSUFFICIENT.

(1) and (2)
If OP = 6 and PQ = 7, 1 < OQ < 13.
INSUFFICIENT.

Hence, E
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Re: In the triangle above, is OQ > 10? (1) OP = 6 (2) PQ = 7  [#permalink]

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08 Nov 2018, 02:52
Both 1 & 2 not sufficient as both individually give information of only one side of the triangle.
Combining two:

If the angle OPQ=90, then by Pythagoras thm, OQ^2= OP^2+PQ^2
Here angle OPQ is obtuse, > 90.
So, OQ^2 > OP^2+PQ^2=36+49=85
OQ can be 10, 11, 12 ( can't be 13 and above since in that case OQ > OP+PQ , which is not possible)
No definite answer for OQ. NOT sufficient. E
Re: In the triangle above, is OQ > 10? (1) OP = 6 (2) PQ = 7   [#permalink] 08 Nov 2018, 02:52
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