PrashantBS Says

Vishal and Anirudh decide to meet at a cafe between 5 pm to 6pm. they agree that the person who arrives first will wait for exactly 15 mins for the other. if each of them arrives at random betwen 5 pm to 6 pm what is the probability that the meeting takes place?

.5 i think so

no i dont understand ur method . plus the answer is potion D .. dont knw how it came though

PrashantBS Says

Vishal and Anirudh decide to meet at a cafe between 5 pm to 6pm. they agree that the person who arrives first will wait for exactly 15 mins for the other. if each of them arrives at random betwen 5 pm to 6 pm what is the probability that the meeting takes place?

is it 323/345 by any chance



??

two cards are drawn from a well shuffled pack of cards one after another .wat is the probability that first frawn card is red and the second is an ace. when the cards that is drawn first is not replaced
1)29/442
2)3/104
3)6/169
4)17/442

Total cases=52*51

fav. cases: First red and non ace and second ace=24*4
First red and ace and second ace=2*3

prob=(96+6)/52*51=1/26=17/442

vyomconfused Says

A&B; together complete a work in 6 min.But A works for 4 min and B works for 6 mins. After this only 1/5 work is remaining.how much time will the slowest person will take to do work all alone?

Pranam vyom bhai____/\____kafi din bad dekhe apko
pranam saurav bhai,bindita____/\____

suppose A does a units of work per min and B does b units
then total work=(a+b)*6
hence (a+b)*6=4a+6b+(a+b)*6/5
hence a/b=3/2
let them be 2x and 3x
hence total work=30x
hence req time=30x/2x=15

two cards are drawn from a well shuffled pack of cards one after another .wat is the probability that first frawn card is red and the second is an ace. when the cards that is drawn first is not replaced
1)29/442
2)3/104
3)6/169
4)17/442

15 min??

1/A + 1/B = 1/6

A&B; work for 4 min in which they can complete 2/3 of the work. After that B alone works for 2 min and complete (4/5 - 2/3) work

So 2/B = 4/5 - 2/3 = 2/15
B = 15 mins

1/A = 1/6 - 1/15
A = 10 mins

So B is slower

Damn such a silly mistake....i took it this way A working indiviually for 4 min and B working indiviually for 6 mins..:banghead:


Anyways thanx.

96 + y^2 = x^2..so 96= x^2-y^2 =(x+y)(x-y)
96=2^5*3..so it can be written as a product of two factors in 0.5*(5+1)*(1+1)= 6 ways..

how did you get 4.?.I guess some out of those 6 will not satisfy the criteria..

yes it can be written as a product of two factors in 6 ways
but both factors has to be even or odd to get integer values of x and y
so subtract 2 cases i.e 1 and 96 and 3 and 32

Vishal and Anirudh decide to meet at a cafe between 5 pm to 6pm. they agree that the person who arrives first will wait for exactly 15 mins for the other. if each of them arrives at random betwen 5 pm to 6 pm what is the probability that the meeting takes place?

When 96 is added to a perfect square, another perfect square is obtained. How many such pairs of perfect squares exist?
1. 4
2. 8
3. 6
4. 12
5. 8

a^2 + 96= b^2
b^2-a^2=96
(b+a) (b-a)=96
Total 4 values satisfy
(5,11),(23,25),(2,10),(10,14)

mkj Says

1!+2!...........+100!/720=...............(remainder??)

1! +.....+ 5!/720

=>153

:)

When 96 is added to a perfect square, another perfect square is obtained. How many such pairs of perfect squares exist?

1. 4
2. 8
3. 6
4. 12
5. 8

N=2 -> 2^2 +96 =10^2
N=5-> 5^2 +96 =11^2
N=10 -> 10^2 +96 =14^2
N=23-> 23^2 +96 -> 25^2

so 4 values satisfy

When 96 is added to a perfect square, another perfect square is obtained. How many such pairs of perfect squares exist?

1. 4
2. 8
3. 6
4. 12
5. 8

4 ??

96 + b^2 = a^2
(a-b)(a+b) = 96 = 2^5*3

(a,b) = (25, 23) (14,10) (10,2) (11,5)

is it opt 1 ... 4 ????

96 + y^2 = x^2..so 96= x^2-y^2 =(x+y)(x-y)
96=2^5*3..so it can be written as a product of two factors in 0.5*(5+1)*(1+1)= 6 ways..

how did you get 4.?.I guess some out of those 6 will not satisfy the criteria..

vyomconfused Says

A&B; together complete a work in 6 min.But A works for 4 min and B works for 6 mins. After this only 1/5 work is remaining.how much time will the slowest person will take to do work all alone?

15 mins


1/10 + 1/15 = 1/6

MKJ Says

1!+2!...........+100!/720=...............(remainder??)

expanding all

1+2+6+24+120+720+720x7+720x7x8.........so rest are 720 multiple

so

1+2+6+24+120=153/720=153 rem

Let the set S = {1, 2, 3, 4, 5, 6, 7, 8}.
Find the number of ordered pairs (A, B), where A and B are subsets of S and A is a proper subset of B.
OPTIONS
1) 6305
2) 6561
3) 4096
4) 6433

Now no. of pairs
(A,B)=8c1(2c0)+(8C2*(2C1))+(8C3*(3C2+3C1))+(8C4(4C3+4c2+4c1)+.....+(8c8(8c7+......+8c1))
=8c2*(2^2-1)+8c3*(2^3-1)+8c4(2^4-1)+8c5(2^5-1)+.....+8c8(2^8-1)
=(8c2*2^2*1^6+..........+8c8*2^8*1^0)-2*(8c2+8c3+8c4+....+8c
=(3^8-8C1*2-1)-1*(2^8-8c1-1)+8c1
=6305

MKJ Says

1!+2!...........+100!/720=...............(remainder??)

6! onwards will be divisible by 720
Hence remainder wd be 1!+2!+3!+4!+5!=153

MKJ Says

1!+2!...........+100!/720=...............(remainder??)

720
2360
2|180
2|90
2|45
3|15
35
6!=6X5X4X3X2X1

Everything after 6!(including 6) is divisible by 720
1!+2!+3!+4!+5!=1+2+6+24+120=153 The ans...

MKJ Says

1!+2!...........+100!/720=...............(remainder??)

all nos from 6! will give remainder 0
so sum of nos till 5! = 153
so remainder 153

MKJ Says

1!+2!...........+100!/720=...............(remainder??)

6! = 720. So remainder 1! + 2! + 3! + 4! + 5! = 153

When 96 is added to a perfect square, another perfect square is obtained. How many such pairs of perfect squares exist?

1. 4
2. 8
3. 6
4. 12
5. 8

is it opt 1 ... 4 ????

vyomconfused Says

A&B; together complete a work in 6 min.But A works for 4 min and B works for 6 mins. After this only 1/5 work is remaining.how much time will the slowest person will take to do work all alone?

15 min??

1/A + 1/B = 1/6

A&B; work for 4 min in which they can complete 2/3 of the work. After that B alone works for 2 min and complete (4/5 - 2/3) work

So 2/B = 4/5 - 2/3 = 2/15
B = 15 mins

1/A = 1/6 - 1/15
A = 10 mins

So B is slower

1!+2!...........+100!/720=...............(remainder??)

vyomconfused Says

A&B; together complete a work in 6 min.But A works for 4 min and B works for 6 mins. After this only 1/5 work is remaining.how much time will the slowest person will take to do work all alone?

A+B=1/6
10A+10B=5/3
AX4+BX6=4/5
10A+15B=2
5B= 1/3
B=1/15
A=1/6-1/15
=5-2/30
A=1/10
B is slower he will take 15 minutes

When 96 is added to a perfect square, another perfect square is obtained. How many such pairs of perfect squares exist?

1. 4
2. 8
3. 6
4. 12
5. 8

Let the set S = {1, 2, 3, 4, 5, 6, 7, 8}.

Find the number of ordered pairs (A, B), where A and B are subsets of S and A is a proper subset of B.
OPTIONS

1)6305
2)6561
3)4096
4)6433

6305.

2 page piche Aizen bhai ne mast samjha diya sum

In how many ways can the natural no's from 1 to 9 be divided into 3 groups of 3 numbers each,such that the sum of the numbers in each group is divisible by 3?
a.9
b.18
c.37
d.38

37..i think so

A&B; together complete a work in 6 min.But A works for 4 min and B works for 6 mins. After this only 1/5 work is remaining.how much time will the slowest person will take to do work all alone?

let the set s = {1, 2, 3, 4, 5, 6, 7, 8}.

Find the number of ordered pairs (a, b), where a and b are subsets of s and a is a proper subset of b.
Options

1)6305
2)6561
3)4096
4)6433

c(8, 1)*(2 - 1) + c(8, 2)*(4 - 1) + c(8, 3)*(2^3 - 1) + ... + c(8, 8 )*(2^8 - 1)
= 3^8 - 1 - (2^8 - 1)
= 6305

Let a,b and c be the positive real numbers. Determine the minimum value of (a+3c)/(a+2b+c) + 4b/(a+b+2c) -8c/(a+b+3c)

Options:
A. 122-17
B. 62-17
C. 122+17
D. 62+17

keep a=b=c=1
1+1-1.6=0.4
so this means c and d cannot be ans.
6*1.4-17=-8.xx
12*1.4=16.8-17=-0.2
let a=1,b=1,c=2
7/5=1.4
4/6=0.666
16/8=2
so=0.0666

So ans. possibly A?? as a , b,c when close are near option A

Let the set S = {1, 2, 3, 4, 5, 6, 7, 8}.

Find the number of ordered pairs (A, B), where A and B are subsets of S and A is a proper subset of B.
OPTIONS

1)6305
2)6561
3)4096
4)6433

10000! = (100!)K P, where P and K are integers. What can be the maximum value of K?



p.s - Warm up question :)

Exponent of 2 in 100! = 97
Exponent of 2 in 10000! = 9995
= 103

Exponent of 97 in 100! = 1
Exponent of 97 on 10000! = 104

So, lower of 103 and 104, i.e, 103 will be the answer

Namaste sabko _____/\______

Hello puys !..
Been long!... I ws out for 3 days !

A set P consists of the first 25 natural numbers. How many minimum numbers should one pick from the set P so that there is always atleast one pair (x,y) among them satisfies 3x=2y?

A: 13 B: 16 C:17 D:18 E:20

is 18 is the answer...???

koi mere bhi ques kardo nahi to muje spam karna padega aise.

10000! = (100!)^K P, where P and K are integers. What can be the maximum value of K?



p.s - Warm up question :)

Shouldn't this question have 100^K*P. Then the answer we can get as 104 as 100! has 24 zeroes and 10000! has 2499 zeroes. Otherwise K can be highest as 101*102*....10000

Hello puys !..
Been long!... I ws out for 3 days !

A set P consists of the first 25 natural numbers. How many minimum numbers should one pick from the set P so that there is always atleast one pair (x,y) among them satisfies 3x=2y?

A: 13 B: 16 C:17 D:18 E:20

Swati04 Says

OA is if C is any number other than 3.

Right if C=3, then (1) - (2) and (2) - (3) becomes identical lines in X-Z plane. Then the point of intersection of all three lines will come out to be a single point.

Whereas if C

Swati04 Says

AIMCAT1317Q:For what values of C does the following system of equations have no solution? i. 2x + y + 3z = 4 ii. 3x + y- z = 5 iii. x + y + 7z = C

iX2 gives 4x+2y+6z=8
substracting 2 -3x-y+z=-5
x+y+7z=3
Therfore c = 3

gs4890 Says

Q:how many natural no:s less than 10^5 have the sum of their digits equal to 10????? options 1)1381 2)1001 3)996 4)252 .

a + b + c + d + e = 10
=> number of solutions = 14C4

but we cannot take a,b,c,d,e > 9

so , 14C4 - 5 = 996

pranam bhai log _____/\____

i - ii/2 = iii

thus, C = 3


cheers :)

OA is if C is any number other than 3.

Swati04 Says

AIMCAT1317Q:For what values of C does the following system of equations have no solution? i. 2x + y + 3z = 4 ii. 3x + y- z = 5 iii. x + y + 7z = C

i - ii/2 = iii

thus, C = 3


cheers

Swati04 Says

AIMCAT1317Q:For what values of C does the following system of equations have no solution? i. 2x + y + 3z = 4 ii. 3x + y- z = 5 iii. x + y + 7z = C

I think it's 3


Approach:


Sum of all the three equations is 6x + 3y + 9z = 9+C

On dividing the equation by 3,it becomes 2x + y + 3z = 3 + C/3

so,when C takes 3,the system of equations have no solution

P.S: I hope the AIMCAT window is over by now;) and Let me know if the answer is wrong

10000! has 2499 zeros
and 100! has 24 zeros

24*104=2496



is it 104....??

341. Mrs. Carson took a taxi to meet her three friends
for lunch. They were waiting for her outside the
restaurant when she pulled up in the car. She
was so excited to see her friends that she left her
tote bag in the taxi. As the taxi pulled away, she
and her friends took notice of the license plate
number so they would be able to identify the car
when they called the taxi company. The four
license plate numbers below represent what each
of the four women thinks she saw.Which one is
most likely the license plate number of the taxi?
a. JXK 12L
b. JYK 12L
c. JXK 12I
d. JXX 12L
342. Zachary has invited his three buddies over to
watch the basketball game on his wide-screen
television. They are all hungry, but no one
wants to leave to get food. Just as they are
arguing about who should make the food
run, a commercial comes on for a local pizzeria
that delivers. The phone number flashes
on the screen briefly and they all try to
remember it. By the time Zachary grabs a
pen and paper, each of them recollects a different
number. Which of the numbers is
most likely the telephone number of the
pizzeria?
a. 995-9266
b. 995-9336
c. 995-9268
d. 995-8266

My takes in BOLD

Is n't this but obvious.
p=1
k = 10000*9999*.....................101

Let a,b and c be the positive real numbers. Determine the minimum value of (a+3c)/(a+2b+c) + 4b/(a+b+2c) -8c/(a+b+3c)

Options:
A. 122-17
B. 62-17
C. 122+17
D. 62+17

Iska answer A hai kya??

10000! = (100!)K P, where P and K are integers. What can be the maximum value of K?



p.s - Warm up question :)

103? as there are 103 times of 100!

Approach:

the largest prime number less than 100 is 97 and 10000! has 103 97's

AIMCAT1317Q:For what values of C does the following system of equations have no solution? i. 2x + y + 3z = 4 ii. 3x + y- z = 5 iii. x + y + 7z = C

Is n't this but obvious.
p=1
k = 10000*9999*.....................101

Let a,b and c be the positive real numbers. Determine the minimum value of (a+3c)/(a+2b+c) + 4b/(a+b+2c) -8c/(a+b+3c)

Options:
A. 122-17
B. 62-17
C. 122+17
D. 62+17

Hello neetu ji....seemed pretty obvious to me too ...but herez the twister.

10000! = (100!)K P, where P and K are integers. What can be the maximum value of K?
=>options for the questions are

a. 104
b. 103
c. 102
d. 105

:)

A square is inscribed in a circle and the circle is inscribed in a regular octagon. Find the ratio of the area of the square to that of the octagon.

plz explain...

area of octagon is = a x (2 + 2 x sqrt 2)

from fig side square and octogon is the same

so ans comes to 1/4.828 ???

dreamz007 Says

yes u r correct now if u can explain in detail :)

It's simple logic..see the question is asked for 'most likely',and NOT the exact detail

From the options of first question,J is only possible option for 1st character

For the 2nd character,3 persons remember it as X,so it's more likely than Y

|ly

K is more likely than X,12 is the only options for next 2 characters and finally L is more likely than I

a. JXK 12L
b. JYK 12L
c. JXK 12I
d. JXX 12L

10000! = (100!)K P, where P and K are integers. What can be the maximum value of K?
p.s - Warm up question :)

Is n't this but obvious.
p=1
k = 10000*9999*.....................101

Let a,b and c be the positive real numbers. Determine the minimum value of (a+3c)/(a+2b+c) + 4b/(a+b+2c) -8c/(a+b+3c)

Options:
A. 122-17
B. 62-17
C. 122+17
D. 62+17

10000! = (100!)K P, where P and K are integers. What can be the maximum value of K?



p.s - Warm up question :)

my take will be

1)4

2) 3

For both of them,the answer is option a?

yes u r correct now if u can explain in detail

if x=-4 then
g(x^2+4x-4)=g(4)

and not g(-4)

how cum u made it g(-4)...????

g(16-16-4)=g(-4)

341. Mrs. Carson took a taxi to meet her three friends
for lunch. They were waiting for her outside the
restaurant when she pulled up in the car. She
was so excited to see her friends that she left her
tote bag in the taxi. As the taxi pulled away, she
and her friends took notice of the license plate
number so they would be able to identify the car
when they called the taxi company. The four
license plate numbers below represent what each
of the four women thinks she saw.Which one is
most likely the license plate number of the taxi?
a. JXK 12L
b. JYK 12L
c. JXK 12I
d. JXX 12L
342. Zachary has invited his three buddies over to
watch the basketball game on his wide-screen
television. They are all hungry, but no one
wants to leave to get food. Just as they are
arguing about who should make the food
run, a commercial comes on for a local pizzeria
that delivers. The phone number flashes
on the screen briefly and they all try to
remember it. By the time Zachary grabs a
pen and paper, each of them recollects a different
number. Which of the numbers is
most likely the telephone number of the
pizzeria?
a. 995-9266
b. 995-9336
c. 995-9268
d. 995-8266

For both of them,the answer is option a?

ans. b)-1

g(h(g(x))=2g(x)^2+3g(x)
g(x^2+4x-4)=2g(x)^2+3g(x)
let x=-4
g(-4)=2g(-4)^2+3g(-4)
0=2g(-4)(g(-4)+1)

g(-4)=-1

if x=-4 then
g(x^2+4x-4)=g(4)

and not g(-4)

how cum u made it g(-4)...????

LOL...SRY IT WAS THE STUPIDEST DOUBT ONE CAN EVER ASK..:p
M OUT OF MY MIND I GUESS..!

my take will be

1)4

2) 3

nah wrong
try again and if u can explain !!

Given that g(h(x)) = 2x + 3x and h(g(x)) = x + 4x 4 for all
real x. WHich of the following could be the value of g(-4)?
a)1 b) -1 c) 2 d) -2 e) -3

ans. b)-1

g(h(g(x))=2g(x)^2+3g(x)
g(x^2+4x-4)=2g(x)^2+3g(x)
let x=-4
g(-4)=2g(-4)^2+3g(-4)
0=2g(-4)(g(-4)+1)

g(-4)=-1