Official Quant thread for CAT 2013

MBA CAT 2024
14183
@IIM-A2013 said:
1)A man earns x% on the first 5000 rupees of his investment and y% on the rest of his investment . If he earns Rs 1250 from Rs 7000 and Rs 1750 from Rs 9000 invested .Find xa)20 b)15c)25d)none
5000*x /100 + 2000*y/100 = 1250

5000*x/100+ 4000*y/100 = 1750
subtract equation 1 from2
==> 20y = 500===> y= 25 ==> x=15
14184
The remainders when F(x) is divided by (x-19) and (x-99) is 99 and 19 respectively. What is the remainder when F(x) is divided by (x-19)(x-99) ?
a) 118-x c) 116-x
b) 80-x d) 40-x
14185
@shattereddream said:
M is a two digit number which has the property that: the product of factorial of its digit>sum of factorial of its digits.how many values of M exists? A)56 B)64 C)63 D)none of these
a! * b! > a! + b! [ Here the case of a=2,b=2 will bring us = sign ]

so a can have values from 2 to 9 and b must be from 3..we cannot have values of b as 2...so c hav values from 3 to 9..so its 8*7 = 56..

if there is greater than or equal to then it will have 64 ...else 56 is the answer
14186
@gupanki2 said:
A student was given 8 two-digit numbers to add, by a teacher. If the student reversed each number and added the results, the sum of the numbers would be 36 more than the actual sum. Find the excess of the sum of the units digits over that of the tens digits.
4 :)
14187

Posting again


A sum of money 2310 is due to be repaid at the end of two yrs. If it has to be repiad in two equal annual instalments (the instalments being paid at the beginning of the yr) at 10% p.a. compounded annually. Find the value of each instalment?

1210
1000
1100
1331

14188
@ravi.theja said:
a! * b! > a! + b! [ Here the case of a=2,b=2 will bring us = sign ]so a can have values from 2 to 9 and b must be from 3..we cannot have values of b as 2...so c hav values from 3 to 9..so its 8*7 = 56..if there is greater than or equal to then it will have 64 ...else 56 is the answer
b will also have value from 2 to 9 how can you count it from 3 , only 0 & 1 will not hold true .
14189
@shattereddream said:
b will also have value from 2 to 9 how can you count it from 3 , only 0 & 1 will not hold true .
2!*2! =4 ; 2! + 2! = 4...?? hw can b be 2 bro?? if its 2 den..it becomes equal not greater than
14190
@vbhvgupta said:
The remainders when F(x) is divided by (x-19) and (x-99) is 99 and 19 respectively. What is the remainder when F(x) is divided by (x-19)(x-99) ?a) 118-x c) 116-x b) 80-x d) 40-x
F(x) can be written as (x-19)(x-99)Q(x) +Ax+B. Find F(19) and F(99) now to find value of A and B as -1 and 118. SO remainder obtained when divided by (x-19)(x-99) is 118-x.

@amresh_maverick said:
Posting againA sum of money 2310 is due to be repaid at the end of two yrs. If it has to be repiad in two equal annual instalments (the instalments being paid at the beginning of the yr) at 10% p.a. compounded annually. Find the value of each instalment?1210100011001331
x=1000. (1.1)^2*x+ 1.1*x = 2310 as the instalments being paid at the beginning of the yr. Solve for x to get each installment value.

1.1*x +x=2310 if installments are collected at end of year.

14191
@pirateiim478 said:
x=1000. (1.1)^2*x+ 1.1*x = 2310 as the instalments being paid at the beginning of the yr. Solve for x to get each installment value.1.1*x +x=2310 if installments are collected at end of year.


Can u explain a bit more?

14192
@ravi.theja said:
2!*2! =4 ; 2! + 2! = 4...?? hw can b be 2 bro?? if its 2 den..it becomes equal not greater than
Another way
sum of factorial of digits will be greater than product of factorial of its digits if at least one of the digits is either 0 or 1.
So, the numbers will be 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91. total = 26 numbers

So, the answer will be the remaining 2 digit numbers = 90 - 26 = 64

14193
@amresh_maverick said:
Can u explain a bit more?
Amount borrowed is present value and amount due is future value .Debt of 2310 due after 2 years means 2310 is future value i.e. you can think, you are depositing your installments in another account so that at end of 2 years it will be 2310.

Simple interest:
Suppose if installment is paid at end of 1st year,it will have interest for 1 year and instllament paid in 2nd year has no interest.

1.1x+x=2310

Similarly if installment is paid at begining of 1st year,it will have interest for 2 years and instllament paid in 2nd year beigining has 1 year interest.

1.2x+1.1x=2310

Compound interest:

At end of year:1.1*x +x=2310
At begining of year :(1.1)^2*x+ 1.1*x = 2310



14194
@Logrhythm thanx mate !
14195
Triangle ABC is inscribed in a circle with center O and radius 6 cm. From a point T, two tangents are drawn, touching the circle at A and C respectively. If angle ACT = 45째 , what is the area in (sq. cm) of the triangle ACT?
14196
@pirateiim478 said:
Triangle ABC is inscribed in a circle with center O and radius 6 cm. From a point T, two tangents are drawn, touching the circle at A and C respectively. If angle ACT = 45째 , what is the area in (sq. cm) of the triangle ACT?
1/2*6*6=18
14197
@pirateiim478 said:
Triangle ABC is inscribed in a circle with center O and radius 6 cm. From a point T, two tangents are drawn, touching the circle at A and C respectively. If angle ACT = 45째 , what is the area in (sq. cm) of the triangle ACT?
is d ans 18. if yes. dan i wud try to explain a bit.
14198
@gnehagarg said:
1/2*6*6=18
@The_Loser said:
is d ans 18. if yes. dan i wud try to explain a bit.
No try again. Options are 3,6,9,NoT
14199

"A milk man starts with a 5 litre can full of milk to deliver milk to his customers. Each of this customers purchases 2 litres of milk from him. After delivering to each of the first two households, he adds 1 litres of water to the can. After giving milk to the third household, instead of adding water, he adds 1 litre of milk and delivers the rest to the fourth and last of his customer. Find the percentage of milk the last customer gets."


options 50%, 60%, 65%, 75%, 80%
14200
How many 10 digit numbers have exactly two digits equal?
14201
@amresh_maverick said:
Posting againA sum of money 2310 is due to be repaid at the end of two yrs. If it has to be repiad in two equal annual instalments (the instalments being paid at the beginning of the yr) at 10% p.a. compounded annually. Find the value of each instalment?1210100011001331
2310(1.1)^2=x(1.1)^2+x(1.1)
2310*1.1=x(1.1)+x
2310*1.1/2.1=x
110*11=x
x=1210
14202
@veertamizhan
@veertamizhan said:
"A milk man starts with a 5 litre can full of milk to deliver milk to his customers. Each of this customers purchases 2 litres of milk from him. After delivering to each of the first two households, he adds 1 litres of water to the can. After giving milk to the third household, instead of adding water, he adds 1 litre of milk and delivers the rest to the fourth and last of his customer. Find the percentage of milk the last customer gets."options 50%, 60%, 65%, 75%, 80%
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