CRACK THE CAT - DOUBT OVER MATHS (PROBLEM SOLVING)

***gaurav200x***

Quote:

Originally Posted by rahul_parab2006

another 1...

PRIME AND COMPOSITE NUMBERS

5) If a and b are two prime numbers, then, a + b can take value :-
1. 78
2. 7
3. 23

Options :
a} 1 Only
b} 2 Only
3} 1 & 2 only
4} 2 & 3 Only

I'm not sure about the direct approach. To solve this, i see the options, hence, i first take 7 = 2+5 is a sum of 2 prime numbers. So, i check whether 78 is possible or not....

2+76 NO
3+75 NO
5+73 YES

So the option should be (3)

***gaurav200x***

One suggestion:

I think it would be better to prepare by starting one topic and posting all the possible types of that particular topic. Since everyone is starting preparation now, so such a methodology will ensure that one topic is thoroughly discussed. It is also better, that one thread is maintained for one topic... eg. One thread on numbers, one thread on Time and Distance.

rahul_parab2006

Quote:

Originally Posted by gaurav200x

One suggestion:

I think it would be better to prepare by starting one topic and posting all the possible types of that particular topic. Since everyone is starting preparation now, so such a methodology will ensure that one topic is thoroughly discussed. It is also better, that one thread is maintained for one topic... eg. One thread on numbers, one thread on Time and Distance.

thanx for giving suggestion, gaurav !
so, likewise, this thread is of numbers, ok...
so my next questions r :- [Q.6 th Q.10]

6) If A, B and C are complex numbers, where A = 3 + 2i, B = 6 – 4i and C = 2 + 6i.
Find the value of b if D is of the form a – bi and D = A + B + C.

a} 0
b}-4
c} 4
d} -1

7) I have 4 diamonds of weight 10, 20, 25 & 30 grams each. What maximum value of weights should I use so as to weigh each one of them accurately, if I am allowed to use just one type of weight?

a} 10 gm
b} 6 gm
c) 5 gm
d} 2 gm

8) In a state 30% of the population are women, 60 % are men and the rest are children. 40 % of the children are enjoying good health, while the rest i.e. 120 are suffering from Thalassemia. Find the total population of that state.

a} 1000
b} 2000
c} 2635
d} 2500

9) The average weight of Indian Cricket team is decreased by 2 kg. when one of the players, weighting 100 kg. replaced by a new player. What is the weight of the new player?

a} 102
b} 78
c} 88
d} 98

10) Mr. X forgets his telephone number. All he remembers is that the 1st digit of the number is an even prime number and the rest of the number is square value of a number having its digits as the first four natural numbers in the regular order. What is his telephone number?

a} 31522756
2} 21567432
3} 21730400
4) 21522756

come'on guyz...give answers and check ur abilty to crack the PS section of the CAT, ...

***gaurav200x***

Quote:

Originally Posted by rahul_parab2006

6) If A, B and C are complex numbers, where A = 3 + 2i, B = 6 – 4i and C = 2 + 6i.
Find the value of b if D is of the form a – bi and D = A + B + C.

a} 0
b}-4
c} 4
d} -1

Answer is 4....

2-4+6

Quote:

Originally Posted by rahul_parab2006

7) I have 4 diamonds of weight 10, 20, 25 & 30 grams each. What maximum value of weights should I use so as to weigh each one of them accurately, if I am allowed to use just one type of weight?

a} 10 gm
b} 6 gm
c) 5 gm
d} 2 gm

Calculate the HCF of 10,20, 25 and 30 which is 5 gm

Quote:

Originally Posted by rahul_parab2006

8) In a state 30% of the population are women, 60 % are men and the rest are children. 40 % of the children are enjoying good health, while the rest i.e. 120 are suffering from Thalassemia. Find the total population of that state.

a} 1000
b} 2000
c} 2635
d} 2500

if population is x. Then 10% of x are children = 0.1 x

60% of 0.1 x = 120

x=2000

Quote:

Originally Posted by rahul_parab2006

9) The average weight of Indian Cricket team is decreased by 2 kg. when one of the players, weighting 100 kg. replaced by a new player. What is the weight of the new player?

a} 102
b} 78
c} 88
d} 98

Answer is 78 kgs... assuming we take 11 player team.

The avg weight is decreased by 2 kg. So, the person should be lighter by total no. of players X 2

Hence the weight must be 100-22 = 78 kgs

Quote:

Originally Posted by rahul_parab2006

10) Mr. X forgets his telephone number. All he remembers is that the 1st digit of the number is an even prime number and the rest of the number is square value of a number having its digits as the first four natural numbers in the regular order. What is his telephone number?

a} 31522756
2} 21567432
3} 21730400
4) 21522756

come'on guyz...give answers and check ur abilty to crack the PS section of the CAT, ...

choice 4.... the sq of 1234 should have 6 at the unit's place!

these questions are good for warm up, but the level of CAT demand's tougher questions.

rahul_parab2006

ya, i know yaar gaurav, but this is a start, aftr some days, i will give u tougher questions...

ur answer to Q. 6 is, unfortunately, wrong !!!

Quote:

Quote:
Originally Posted by rahul_parab2006
6) If A, B and C are complex numbers, where A = 3 + 2i, B = 6 – 4i and C = 2 + 6i.
Find the value of b if D is of the form a – bi and D = A + B + C.

a} 0
b}-4
c} 4
d} -1

Answer is 4....

2-4+6

answer :
A + B+ C = 3 + 2i + 6 - 4i + 2 + 6i
= 3 + 6 + 2 + (2 - 4i + 6i)
= 11 + 4i
= 11 - (-4i)

Therefore, b = -4.
Hence, 2

All other answers (from Q. 7 to Q. 10) r rite...

@ gaurav, plz don't give answers quickly aftr i posted it...
let others ( mp members) give answers !!!
Good luck for next questions...!

rahul_parab2006

DIVISIBILITY TEST

1. What is the value of A if 305143A2 is divisible by both 9 & 4?

1] 3
2] 5
3] 7
4] 9

HCF & LCM

2. Find the LCM of the largest 2 digit integer, the square of eleven, and the square of nine.

1] 9801
2] 1089
3] 8019
4] 6561

3. The HCF of two fractions is 1/144 and their product is 7/ 36. Find their LCM.

1] 1/12
2] 14
3] 28
4] None of these

4. P is the set of prime factors of 7040 and Q is the set of prime factors of 4180. If x is a member of set P and y is a member of set Q. What is the greatest possible value of y-x?

1] 14
2] 17
3] 8
4] None of these

BASIC ALGBRIC FORMULAE

5. Which of the following is true?
I) Every odd number can be expressed as a difference of the squares of two consecutive whole numbers.
II) Every even number can be expressed as a difference of the squares of two whole numbers
III) Sum of a number, its square and the successor of the number will give the square of the successor of the number.

1] I or II
2] I or III
3] I & III
4] I, II & III

***gaurav200x***

Quote:

Originally Posted by rahul_parab2006

ya, i know yaar gaurav, but this is a start, aftr some days, i will give u tougher questions...

ur answer to Q. 6 is, unfortunately, wrong !!!

answer :
A + B+ C = 3 + 2i + 6 - 4i + 2 + 6i
= 3 + 6 + 2 + (2 - 4i + 6i)
= 11 + 4i
= 11 - (-4i)

Therefore, b = -4.
Hence, 2

All other answers (from Q. 7 to Q. 10) r rite...

@ gaurav, plz don't give answers quickly aftr i posted it...
let others ( mp members) give answers !!!
Good luck for next questions...!

thanks, i dint see that.......... in the haste of doing the work, i overlooked the -ve sign...

Will remember the 2nd thing.

***gaurav200x***

Quote:

Originally Posted by rahul_parab2006

DIVISIBILITY TEST

1. What is the value of A if 305143A2 is divisible by both 9 & 4?

1] 3
2] 5
3] 7
4] 9

HCF & LCM

2. Find the LCM of the largest 2 digit integer, the square of eleven, and the square of nine.

1] 9801
2] 1089
3] 8019
4] 6561

3. The HCF of two fractions is 1/144 and their product is 7/ 36. Find their LCM.

1] 1/12
2] 14
3] 28
4] None of these

4. P is the set of prime factors of 7040 and Q is the set of prime factors of 4180. If x is a member of set P and y is a member of set Q. What is the greatest possible value of y-x?

1] 14
2] 17
3] 8
4] None of these

BASIC ALGBRIC FORMULAE

5. Which of the following is true?
I) Every odd number can be expressed as a difference of the squares of two consecutive whole numbers.
II) Every even number can be expressed as a difference of the squares of two whole numbers
III) Sum of a number, its square and the successor of the number will give the square of the successor of the number.

1] I or II
2] I or III
3] I & III
4] I, II & III

1) Shud be divisible by 36 and hence answer is 7
2) u need the LCM of 99, 121 and 81 = 9801
3) answer is 28 hcf X lcm = product of nos.
4) the answer is none of these. The greatest possible value of y is 209 and the least value of x would be 2
5) i think its (2) I or III
every odd no. can be expressed except 1

rahul_parab2006

ANSWERS ARE :-
1) 4] 9
2) 1] 9801
3) 3] 28
4) 2] 17
5] 3] I or III

Gaurav, u r rite in Q. No. 2, 3 & 5.
But, u get wrong answer in Q.1 & Q.4.

Try again...
give explanation...
good going...

***gaurav200x***

Quote:

Originally Posted by rahul_parab2006

ANSWERS ARE :-
1) 4] 9
2) 1] 9801
3) 3] 28
4) 2] 17
5] 3] I or III

Gaurav, u r rite in Q. No. 2, 3 & 5.
But, u get wrong answer in Q.1 & Q.4.

Try again...
give explanation...
good going...

how can i be wrong in the 1st one... the last digits have to be 72 to be divisible by 3. 32, 52 or 92 can't be

and for the last one... I too thought about I and III but i dun think I is completely true... bcoz 1 is not included.