Official Quant thread for CAT 2013

@hiteshkhurana82 said:
If the largest angle in a triangle is 70o, what is least possible value of the smallest angle of the triangle?69o1o40o39o41o
40 ?
@tmohan02 said:
What will be the the unit's digit of (1273)^122! ?Soln (given in the Arun Sharma: 122! is a number of the form 4n. Hence the answer should be 1.I don't undersand this..... Plzexpalin.
check the cyclicity.

Alternate method:
We have to find out (1273)^122! mod 10
=(3)^122! mod 10
=(3)^0 mod 10 {E(10)=4, 122! mod 4=0}
=1 mod 10
@tmohan02 said:
What will be the the unit's digit of (1273)^122! ?Soln (given in the Arun Sharma: 122! is a number of the form 4n. Hence the answer should be 1.I don't undersand this..... Plzexpalin.
122! mod 4 =0

so 3^4=81 so ans =1
@tmohan02 said:
What will be the the unit's digit of (1273)^122! ?Soln (given in the Arun Sharma: 122! is a number of the form 4n. Hence the answer should be 1.I don't undersand this..... Plzexpalin.
122! will be always divide by 4..
so 122! mod 4 = 0
3^0=1
@sujamait said:
Let N be the number of ways in which 2010 can be written in the form,2010 = 1000a3 + 100a2 + 10a1 + a0, where ai, for 0 ≤ i ≤ 3, is an integer and 0 ≤ ai ≤99.An example of such representation is, 2010 = 1 × 10^3 + 9 × 10^2 + 11 × 10^1 + 0 × 10^0Find N.OPTIONS1) 2 2) 3 3) 52 4) 202 5) None of the above
1000x + 100y + 10z + w = 2010

x = 2,
10z + w = 1, so 2 ways

x = 1,
100y + 10z + w = 1010
y = 0, 10z + w = 1010, 8 ways
y = 1, 10z + w = 910, 10 ways
.
y = 9, 10z + w = 110, 10 ways
y = 10, 10z + w = 10, 2 ways
total = 100 ways

x = 0
100y + 10z + w = 2010
y = 10, 11, 12, ..., 20
case will be same as x = 1

So, total 2 + 100 + 100 = 202 ways
@sujamait said:
Let N be the number of ways in which 2010 can be written in the form,2010 = 1000a3 + 100a2 + 10a1 + a0, where ai, for 0 ≤ i ≤ 3, is an integer and 0 ≤ ai ≤99.An example of such representation is, 2010 = 1 × 10^3 + 9 × 10^2 + 11 × 10^1 + 0 × 10^0Find N.OPTIONS1) 2 2) 3 3) 52 4) 202 5) None of the above
Clearly (a3)

1) a3 = 2

10 = 100a2 + 10a1 + a0

=> a2 has to be zero => 10a1 + a0 = 10 => 2 cases

2) a3 = 1

1010 = 100a2 + 10a1 + a0

a2 = 0 => 10a1 + a0 = 1010 => a1 = 92 to 99 (8 cases)
a2 = 1 => 10a1 + a0 = 910 => a1 = 82 to 91 (10 cases)
a2 = 2 => 10a1 + a0 = 810 => a1 = 72 to 81 (10 cases)
and so on..

a2 = 9 => 10a1 + a0 = 110 => a1 = 2 to 11 (10 cases)
a2 = 10 => 10a1 + a0 = 10 => 2 cases

3) a3 = 0

2010 = 100a2 +10a1 + a0

Max value of 10a1 + a0 can be 1089, so min value for a2 = 10

a2 = 10 => 10a1 + a0 = 1010 => 8 cases (same as case when a3 = 1)
...similar cases will come up here too (as in case of a3 = 1)

So, total cases = 2 + (8 +2 + 10*9)*2 = 202 ?
@chillfactor said:
1000x + 100y + 10z + w = 2010x = 2,10z + w = 1, so 2 waysx = 1,100y + 10z + w = 1010y = 0, 10z + w = 1010, 8 waysy = 1, 10z + w = 910, 10 ways.y = 9, 10z + w = 110, 10 waysy = 10, 10z + w = 10, 2 waystotal = 100 waysx = 0100y + 10z + w = 2010y = 10, 11, 12, ..., 20case will be same as x = 1So, total 2 + 100 + 100 = 202 ways
@YouMadFellow said:
Clearly (a3) 1) a3 = 210 = 100a2 + 10a1 + a0 => a2 has to be zero => 10a1 + a0 = 10 => 2 cases2) a3 = 11010 = 100a2 + 10a1 + a0a2 = 0 => 10a1 + a0 = 1010 => a1 = 92 to 99 (8 cases)a2 = 1 => 10a1 + a0 = 910 => a1 = 82 to 91 (10 cases)a2 = 2 => 10a1 + a0 = 810 => a1 = 72 to 81 (10 cases)and so on.. a2 = 9 => 10a1 + a0 = 110 => a1 = 2 to 11 (10 cases)a2 = 10 => 10a1 + a0 = 10 => 2 cases3) a3 = 02010 = 100a2 +10a1 + a0Max value of 10a1 + a0 can be 1089, so min value for a2 = 10a2 = 10 => 10a1 + a0 = 1010 => 8 cases (same as case when a3 = 1)...similar cases will come up here too (as in case of a3 = 1)So, total cases = 2 + (8 +2 + 10*9)*2 = 202 ?
sahi hai yaro..but exam mein yeh Q last mein hee karne types lag rha hai..
@sujamait said:
sahi hai yaro..but exam mein yeh Q last mein hee karne types lag rha hai..
Once you know the approach, it won't take much time :). All these type of questions have the same method of rotating the integers in a range. The number of cases always tend to follow a pattern, if they don't, then leave it 😛

Guys, how do i edit my post....often i have to double post or accidentally double post, since there's no edit button..

Average cost of 5 apples and 4 mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the total cost of 24 apples and 24 mangoes.
a) Rs.1044
b) RS.2088
c)Rs.720
d) Rs.324

can u pls solve this??
hi friends can u tell me ..doing mba after bachelor degree is better or after 2 years job experience?
@viddu said:
Average cost of 5 apples and 4 mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the total cost of 24 apples and 24 mangoes.a) Rs.1044 b) RS.2088 c)Rs.720 d) Rs.324can u pls solve this??
5a + 4m = 36*9

7a + 8m = 48*15

Adding,we get 12*(a + m) = 36*9 + 48*15

Now, 24*(a + m) = 2*36*(9 + 20) = 72*29 = 2088 ?
@viddu said:
Average cost of 5 apples and 4 mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the total cost of 24 apples and 24 mangoes.a) Rs.1044 b) RS.2088 c)Rs.720 d) Rs.324can u pls solve this??
Avg cost of 5 apples and 4 mangoes = Rs. 36
Total cost = 36 * 9 = 324

Avg cost of 7 apples and 8 mangoes = 48
Total cost = 48 * 15 = 720

Total cost of 12 apples and 12 mangoes = 324 + 720 = 1044
Therefore, cost of 24 apples and 24 mangoes = 1044 * 2 = 2088
@viddu said:
hi friends can u tell me ..doing mba after bachelor degree is better or after 2 years job experience?
Not the right thread to discuss this :nono: . Search for specific threads on this topic.
@viddu said:
Average cost of 5 apples and 4 mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the total cost of 24 apples and 24 mangoes.a) Rs.1044 b) RS.2088 c)Rs.720 d) Rs.324can u pls solve this??
2088?
@shattereddream
Thank u:)
@anantn said:
Guys, how do i edit my post....often i have to double post or accidentally double post, since there's no edit button..
There is an edit option. Move your mouse to the top of the post. A minus sign will appear. Click that , and then edit :)
@viddu said:
hi friends can u tell me ..doing mba after bachelor degree is better or after 2 years job experience?
Ask your query here
http://www.pagalguy.com/discussions/2012-which-b-schools-should-you-apply-to-25083927/3594168

Going with a experience is also good......... Different college different perception.
@viddu said:
Average cost of 5 apples and 4 mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the total cost of 24 apples and 24 mangoes.a) Rs.1044 b) RS.2088 c)Rs.720 d) Rs.324can u pls solve this??
5A+4M=36*9
7A+8M=48*15
adding these two

12A+12M=1044
24A+24M=2088?
@viddu said:
Average cost of 5 apples and 4 mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the total cost of 24 apples and 24 mangoes.a) Rs.1044 b) RS.2088 c)Rs.720 d) Rs.324can u pls solve this??
5a + 4m = 36*9 ------1
7a + 8m = 48*15-------2
2( 1+2 )
=> 2088