In circle O above, MN NO. All of the following must be true EXCEPT

Question

https://gmatclub.com/forum/download/file.php?id=39995 In circle O above, MN > NO. All of the following must be true EXCEPT (A) MN < 2MO (B) x > y (C) z = y (D) x = y + z (E) x > 60° 2018-02-14_0950.png

varun4s · Answer

Given: MN>NO

But OM=ON

Therefore, MN>MO....(1)

Option A MN< 2MO can never be possible.

Answer: A.

PraveenChahal · Answer

Option D may or may not be true. All others are possible

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PraveenChahal · Answer

Option A is possible because Diameter of the circle will always be greater than the arc in a semi circle

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niks18 · Answer

(A) MN < 2MO----- any cord that does not pass through the center has to be less than the diameter. True (B) x > y ---- angle opposite to the greater side is greater. given MN>NO (or OM). True (C) z = y ----- NO=OM=radius; hence z=y. True (D) x = y + z -----This may or may not be true. if x=90, then y=z=45, we have a YES but if x=100 then y=z=40 and we have a NO. Not always true (E) x > 60° ----- if x=60, then y=z=60 but given MN>NO so equilateral triangle is not possible. x cannot be less than 60 because in that case y & z both will be greater than x implying MN60. True Answer: Option D

niks18 · Answer

Hi  varun4s

Question says which is  NOT ALWAYS TRUE . The highlighted portion is incorrect. Diameter is the biggest cord in the circle.

OC2910 · Answer

we know MN >ON therefore we get two things angle X is largest
now checking options 
A)MN<2ON (this has to be true :sum of two side greater than third)
B)we already deduced
C)we already know
D)doubtful not necessary hold
E)must be true as MN is greater we cannot make adjustments to MN as MN will become shorter than NO

D is answer IMO

pushpitkc · Answer

https://gmatclub.com/forum/download/file.php?id=39995 First step to solving problems such as this is decoding the stem. Here, must be true EXCEPT means that we need to find that option which is not always necessarily true. RULE: The angle opposite to the largest side is the largest angle (A) MN < 2MO The longest chord in a circle is the diameter. Therefore, MN(another chord) < 2MO(diameter) (B) x > y Since MN > NO, this statement is always true (C) z = y The angles opposite to the equal side are always equal. z and y are the angles opposite to the radii and will always be equal (D) x = y + z This statement is true only when x=90 and y=z=45. For any other measure of x,y,and z this statement is not necessarily TRUE . (E) x > 60° if x\le60° the radius(MO/NO) of the triangle is greater than the chord which is not possible. We are given that MN > NO, so this statement is always true Therefore, Option D(x=y+z) is not necessarily true!

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In circle O above, MN > NO. All of the following must be true EXCEPT

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