Official Quant thread for CAT 2013

MBA CAT 2024
9901

How many 3 digit numbers leave a remainder of 4 when divided by 21 and a remainder of 8 when divided by 13 ?

9902
@nole said:
How many 3 digit numbers leave a remainder of 4 when divided by 21 and a remainder of 8 when divided by 13 ?
No. Should be in the form of 151+273K Where k can take value 0,1,2,3

So only Four numbers 151 ,424,697,970 are possible
9903
@Aman.Malhotra 151 + 273k.How did you get that expression?
9904
@nole http://www.pagalguy.com/discussions/conceptstotal-fundas-25023536/784613
Post No. 17
9905
@nole said:
How many 3 digit numbers leave a remainder of 4 when divided by 21 and a remainder of 8 when divided by 13 ?
N = 21k + 4 = 13n + 8
13n = 13k + (8k - 4)
(8k - 4) is multiple of 13
k = 13a + 7

N = 273a + 151
9906
@chillfactor In the 4th line how did u get k=13a+7 ?
9907
Find next term

1,3,11,67,535


(for those who have attempted this earlier, pls dnt reply)
9908
@bullseyes said:
Find next term 1,3,11,67,535 (for those who have attempted this earlier, pls dnt reply)
5351?
9909
@19rsb said:
5351?
approach?
9910
@bullseyes said:
approach?
1
1*2+1=3
3*4-1=11
11*6+1=67
67*8-1=535
535*10+1=5351

9911
@gkkshetija said:
one merchant correctly calculates his profit percentage on the cost price ;another wrongly calculates it on the selling price. find the diffrence in the actual profit if both claim to make30% profit and their revennue is Rs. 3900.
1st merchant:
(3900-x)/x=30/100
x=3000
2nd merchant:
(3900-y)/3900=30/100
y=2730
Difference=3000-2730=270
9912
@nole said:
How many 3 digit numbers leave a remainder of 4 when divided by 21 and a remainder of 8 when divided by 13 ?
4 numbers?

N = 21a + 4 = 13b + 8
21a = 13b + 4
b = (21a - 4)/13

Find integral values for 'a' to get integral values for 'b'.
a = 7,20,27,... = 7 + 13k

N = 21(7 + 13k) + 4
= 147 + 273k + 4
= 273k + 151

Put k = 0,1,2,3
N = 151, 424, 697, 970
9913

Find the remainder when 54^124 is divided by 17?

a. 4 b. 5 c. 13 d. 15

9914
@anilapex said:
Find the remainder when 54^124 is divided by 17?a. 4 b. 5 c. 13 d. 15
4?
9915
@htomar said:
7 is a prime number.. so euler number for 7 = 6so (51^203/7)R = (51^5/7)R = (2^5/7)R = (32/7)R =4

Thanks

Euler method for finding remainder needs less calculation than the method given in Quant (Arun Sharma)

What's Euler number & how to find remainder by this method?
9916
@19rsb Yes

you've a shortcut for this?


I solved it correctly but it was lengthy

If you've know a shorter method, please share it
9917
@anilapex said:
Find the remainder when 54^124 is divided by 17?a. 4 b. 5 c. 13 d. 15
should be 4.

use Euler's remainder theorem
9918
@anilapex said:
Find the remainder when 54^124 is divided by 17?a. 4 b. 5 c. 13 d. 15
54^124 mod 17
Euler of 17=16
Hence 54^124=54^112*54^12 mod 17
54^12 mod 17=3^12 mod 17
(-4)^3 mod 17=(-1*-4) mod 17=4
9919
@anilapex said:
@19rsb Yes you've a shortcut for this?I solved it correctly but it was lengthy If you've know a shorter method, please share it
Euler is a shortcut in itself
R(54^124/17)=R(3^124/17).........I
E(17)=16
NOW R(124/16)=12
HENCE , I REDUCES TO R(3^12/17)=R(81^3/17)=R(-4^3/17)
R(-4*-1/17)=4
9920
@anilapex said:
Find the remainder when 54^124 is divided by 17?a. 4 b. 5 c. 13 d. 15
51 mod 17 = 0

(51 + 3)^124 mod 17 = 3^124 mod 17 = 3^12 mod 17 (as E(17) = 16) => 81^3 mod 17
= (-4)^3 mod 17 = 4