Question from MockCat, SimCat, Aim Cat,...... for CAT'06

kabir1224

Hey guys i think this new thread is a great oppurtunity n i would say lets make it a grand success by contributing and gaining as much as v can. My first contribution might be simple but i found it to be usefull.
Here it goes:
1) How many integers n are there such that 2<=n<=1000 and the highest common factor of n and 36 is 1?
a)166 b)332 c)361 d)416

Mr. Sharma picks up his son daily by his car after the son's school gets over. They(Mr. Sharma & his son) reach home exactly at 5pm everyday. On a particular day the son's school got over one hour earlier than the scheduled time & hence he started walking with the speed of 3km per hr towards his home. Mr Sharma met his son on the way to school and they reached home at 4.45 pm on that day.

2) What is the speed of Mr. Sharma's car?
a) 15Kmph b)21Kmph c)28Kmph d)36Kmph

3) How long did Mr.Sharma's son walk?
a)45.7 mins b)36.7 mins c)52.5 mins d)72.5 mins

anirban_ju

My answer to Q1 is b)332.
My answer to Q2 is b)21 Kmph
My answer to Q3 is c)52.5 mins

dilton

good thread man!

kabir1224

Quote:

Originally Posted by anirban_ju

My answer to Q1 is b)332.
My answer to Q2 is b)21 Kmph
My answer to Q3 is c)52.5 mins

Bulls eye you got all ques correct. keep up the good work dude

sundar_cts

Quote:

Originally Posted by anirban_ju

My answer to Q1 is b)332.
My answer to Q2 is b)21 Kmph
My answer to Q3 is c)52.5 mins

Can you please explain the steps for Q2 and Q3?

balajifire

guys as it said earlier.. people from CL and any other institute other than TIME and IMS to come forward.
since we find many persons from TIME and IMS.

guys i would like to ask if anybody can post their AIMCATS or SImcats...on this thread. it would help all.......

crazyfootballer

Quote:

Originally Posted by kabir1224

Hey guys i think this new thread is a great oppurtunity n i would say lets make it a grand success by contributing and gaining as much as v can. My first contribution might be simple but i found it to be usefull.
Here it goes:
1) How many integers n are there such that 2<=n<=1000 and the highest common factor of n and 36 is 1?
a)166 b)332 c)361 d)416

Mr. Sharma picks up his son daily by his car after the son's school gets over. They(Mr. Sharma & his son) reach home exactly at 5pm everyday. On a particular day the son's school got over one hour earlier than the scheduled time & hence he started walking with the speed of 3km per hr towards his home. Mr Sharma met his son on the way to school and they reached home at 4.45 pm on that day.

2) What is the speed of Mr. Sharma's car?
a) 15Kmph b)21Kmph c)28Kmph d)36Kmph

3) How long did Mr.Sharma's son walk?
a)45.7 mins b)36.7 mins c)52.5 mins d)72.5 mins

1. Here, n can only be odd. But 36 has 3 as factor hence we need to subtract ood nos. which are multiple of 3 from the total no. of odd nos. from 2 to 1000.

Total odd nos. = 499
No. of multiples of 3 = 333. Out of which 167 are odd.
Hence n take 499-167=332 values.

Q2 and Q3 - Somebody pls explain how to do such kinda questions. I am unable to solve them

Quagmire

Quote:

Originally Posted by crazyfootballer

1. Here, n can only be odd. But 36 has 3 as factor hence we need to subtract ood nos. which are multiple of 3 from the total no. of odd nos. from 2 to 1000.

Total odd nos. = 499
No. of multiples of 3 = 333. Out of which 167 are odd.
Hence n take 499-167=332 values.

Q2 and Q3 - Somebody pls explain how to do such kinda questions. I am unable to solve them

crazyfootballer, I'm not sure about the solution of the first question. Because out of the 333 multiples of 3 till 1000, 167 are odd => the other 166 remaining are even. But still the even nos here are multiples of 3, right? Then how can their HCF with 36 give 1? I may be wrong here. If yes, then plz correct me.

warrior

Quote:

Originally Posted by kabir1224

Hey guys i think this new thread is a great oppurtunity n i would say lets make it a grand success by contributing and gaining as much as v can. My first contribution might be simple but i found it to be usefull.
Here it goes:
1) How many integers n are there such that 2<=n<=1000 and the highest common factor of n and 36 is 1?
a)166 b)332 c)361 d)416

Mr. Sharma picks up his son daily by his car after the son's school gets over. They(Mr. Sharma & his son) reach home exactly at 5pm everyday. On a particular day the son's school got over one hour earlier than the scheduled time & hence he started walking with the speed of 3km per hr towards his home. Mr Sharma met his son on the way to school and they reached home at 4.45 pm on that day.

2) What is the speed of Mr. Sharma's car?
a) 15Kmph b)21Kmph c)28Kmph d)36Kmph

3) How long did Mr.Sharma's son walk?
a)45.7 mins b)36.7 mins c)52.5 mins d)72.5 mins

hi are these from any mocks AIMCAT,SIMCAT ......? If not then you could have posted in some other thread. This thread is only for mocks questions.

crazyfootballer

Quote:

Originally Posted by Quagmire

crazyfootballer, I'm not sure about the solution of the first question. Because out of the 333 multiples of 3 till 1000, 167 are odd => the other 166 remaining are even. But still the even nos here are multiples of 3, right? Then how can their HCF with 36 give 1? I may be wrong here. If yes, then plz correct me.

This is what I am saying. We need to find the nos. whose HCF with 36 is 1. So, no question of even nos. comes into picture. We are just looking for odd nos which are not multiples of 3 for our solution.

Total odd nos. = 499
Toal multiples of 3 = 333
now, out of 333 multiples of 3 we are concerned with only odd multiples of 3 which are equal to 167 (bcoz we have already discarded even nos, in other words in 499 nos. we are not talking abt even nos. at all).

Hence we need to subtract these 167 odd multiples of 3 from 499 as HCF of these nos. with 36 is 3.

Our answer thus is 499-167=332