DS & Problem solving questions

[astrerix]

DS questions

 

1. Is the average of ten integers greater than 10?

(1) Half of the integers are greater than 10

(2) Half of the integers are less than 10

 

2. Is A > B?

(1) AX > BX

(2) X

 

 

 

Problem solving

 

1. Which of the following must be true?

I. Any two lines which are parallel to a third line are also parallel to each other

II. Any two planes which are parallel to a third plane are parallel to each other

III. Any two lines which are parallel to the same plane are parallel to each other

(A) I only

(B) II only

© I and II only

(D) II and III only

(E) I, II and III

[thebullfighter]

First is E.

 

The other 5numbers could be just anything...

say with Stat1: sum of other 5 is just 5... or may be it's 5000000 ie not known..

again stat2: given sum

 

Second is C

from 1: X could be -ve or +ve.. not sufficient Given in stat2.

 

PS-- C

 

1&2 are easy.. though ask if not clear, some1 will xplain.

 

3--- line parallel to plane is that the plane of line is parallel to the other plane, and within that plane, two lines may be parallel.. or may not be...

[astrerix]

2. Is A > B?

(1) AX > BX

(2) X

 

Hi thebullfighter,

 

You said >

 

My answer is E. If it was stated that A & B was +ve I would have agreed with answer as C, but its not stated that A & B are +ve.

Pl. correct me if I am wrong.

[thebullfighter]

oops soo sorry.. i was lost.. hd my mind somewhere else..

You are absolutely right sir..

 

(thebullfighter said: "1&2 are easy.. though ask if not clear, some1 will xplain." :D ) now th answers r confirmed.. got the OAs right... Hope was fine with other explanations...

[awais]

I think 2 is C, the two together tell us that A

[sunilbhat]

For question 2 I also support the explanation of . Let's assume A = 2 ,B = 3

and x = -1

AX = -2, BX = -3.

AX > BX, thus satisfying the statement 1. .Here A

 

Now A = -2 and B = -3. Here A > B

AX = 2, BX = 3. It doesn't satisfy statement 1.

 

Now A = 3, and B = 2

AX = -3, BX=-2. It again doesn't satisfy statement 1

 

Now A=-3, B = -2 Here A

AX = 3, BX = 2. It does satisfy statement 1

 

Now from above we see that taking too statements together we always get A

Therefore the answer should be C

[asd123]

SunilBhatt,

for Q2

Shouldn't your answer be E, since from the explanation you have given it seems like you cannot conclude if A>B reliably.

 

Answer for Q 3 - A

[thebullfighter]

asd123 "Q3-A"... can u pls explain...

 

According to me, it should hav been... C ie stat 1&2 are true.. but third not necessary... I hav given my explanation before...

[sunilbhat]

If you read my explanation carefully it says that if x BX only if A

[thebullfighter]

yap, i also realised tht latr.. as posted...

 

BTW pls clear the debate on Q3, if u have idea...

[sunilbhat]

In Q 3 I think statements 2 is illogicall. How can 2 planes be parallel to a 3rd plane. We have only X,Y, and Z planes, and all three are perpendicular to each other

[asd123]

take my answer back , i think it should be c

[thebullfighter]

asd123 i was soo sure bout that1, my geometry is pretty fine.... u think right..

 

btvn sunil.. :)

 

 

consider two rooms in your house with a common wall between them...

 

the wall in room1 opposite to that common wall be PlaneX, the Common wall be PlaneY and the wall in room2 opposite to the common wall be PlaneZ

(assuming rooms to be proportional and ideal case...)

 

Then it's said that Plane X, Y and Z are parallel to each other.... ;)

[sunilbhat]

That means E should be the answer for Q 3

[pleekha]

Ans for Q 3 is C.

for III even two perpedicular lines can be parallel to a plane. Visualize it in

3-d.

 

for Q 2 by both statement A

[thebullfighter]

asd123 i was soo sure bout that1, my geometry is pretty fine.... u think right..

 

btvn sunil.. :)

 

 

consider two rooms in your house with a common wall between them...

 

the wall in room1 opposite to that common wall be PlaneX, the Common wall be PlaneY and the wall in room2 opposite to the common wall be PlaneZ

(assuming rooms to be proportional and ideal case...)

 

Then it's said that Plane X, Y and Z are parallel to each other.... ;)

That means E should be the answer for Q 3

I thought that an explanation so clearly defined will clear all doubts.. :rolleyes:

 

Sunil, Q asks about lines not planes... Now Consider a line on Plane 1, at 30degree to the floor... Another on Plane 2, which is at 120degree to floor.. NOW as PLane 1,2,3 are parallel... Lines are parallel to plane 3 but not to each other... (form a kind of cross... try holding three papers parallel to each other, and draw lines on them at different angles.... i think thats max i can do... )