Official Quant thread for CAT 2013

MBA CAT 2024
5861
@19rsb said:
(20^2004) + (16^2004) - (3^2004) - 1 is divisible by?1)3172)3233)2534)91
2)323

20^2004 - 3^2004 + 16^2004 - 1^2004
=(20 - 3)(20 + 3)(20^2 + 3^2)...(20^1002 + 3^1002) + (16 - 1)(16 + 1)(16^2 + 1^2)...(16^1002 + 1^1002)
= (17)(23)(20^2 + 3^2)...(20^1002 + 3^1002) + (17)(15)(16^2 + 1^2)...(16^1002 + 1^1002)

20^2004 - 1^2004 + 16^2004 - 3^2004
= (19)(21)(20^2 + 1^2)...(20^1002 + 1^1002) + (13)(19)(16^2 + 3^2)...(16^1002 + 3^1002)

From the above equations it is clear that the given expression is divisible by both 17 and 19

So 17*19 = 323
5862
@19rsb said:
(20^2004) + (16^2004) - (3^2004) - 1 is divisible by?1)3172)3233)2534)91
323
323=17*19
Take Euler nd reduce power
all trms cancel out
5863
@19rsb said:
(20^2004) + (16^2004) - (3^2004) - 1 is divisible by?1)3172)3233)2534)91
a^n - b^n is always divisible by a - b.
a^n - b^n is always divisible by a + b when n is even.

Therefore, (20^2004 - 3^2004) + (16^2004 - 1^2004) is divisble by 17

and (20^2004 - 1^2004) + (16^2004 - 3^2004) is divisble by 19

whole expression is divisible by 17*19 = 323
5864
@ScareCrow28 ya i figured it out but try this one 108/1330 and 106/1284...its in 1 of DI questions.
5865
@sonic_boom said:
The ratio of monthly income of A and B is 3:4.the ratio of monthly expenditure of A and B is 4:5 . Wat should be the ratio of saving of A and B.OA 13:20
Ia = 3x, Ib = 4x
Ea = 4y, Eb = 5y
Ratio of savings = (Ia - Ea)/(Ib - Eb)
= (3x - 4y)/(4x - 5y)

The questions seems to be incomplete or the problem has to be solved by looking at the options.
5866
@quant89 said:
Can any1 help me with easiest way to compare 497/3189 and 483/3230 for greater value b/w them....is der any trick to solve such calculations...or make such comparisons...pls help
in this case its clearly evident that first ratio is greater
General case
% change in numerator from 497 to 483 = 14/497 approx 14/500= 2.8% decrease
%change in denominator from 3189 to 3230 = 41/3189 approx 40/3190=4/319 approx 4/320= 1.25% increase
so numerator decreased more than the denominator increase so second is smaller
5867
@quant89 said:
@ScareCrow28 ya i figured it out but try this one 108/1330 and 106/1284...its in 1 of DI questions.
from 108 to 106 there is a decrease of 2/108 percent = 8/432 (EDITED)
from 1330 to 1284 there is a decrease of 16/1330 percent = 8/665

Clearly the denominator has decreased less than the numerator.

So 108/1330
5868
@grkkrg said:
Ia = 3x, Ib = 4xEa = 4y, Eb = 5yRatio of savings = (Ia - Ea)/(Ib - Eb)= (3x - 4y)/(4x - 5y)The questions seems to be incomplete or the problem has to be solved by looking at the options.
yeah, i also think the question is incomplete, but the guy who gave me this questions says it's complete.
5869
@quant89 said:
@ScareCrow28 ya i figured it out but try this one 108/1330 and 106/1284...its in 1 of DI questions.
108/1330 = (106*1.02)/(1284*1.04) ---- (approx)
=> 108/1330 = 106/1284 * (Hence second is bigger...
5870
@sonic_boom said:
The ratio of monthly income of A and B is 3:4.the ratio of monthly expenditure of A and B is 4:5 . Wat should be the ratio of saving of A and B.OA 13:20
It is a question from the TIME booklet and it had 4 options, out of which 3 got eliminated :/
5871
@gautham87
@rkshtsurana said:
@gautham872.149^646 = 1 mod 647149^149226 = 1 mod 647149^3 N -1 = 0 mod 6473307949*N -1 should be divisible by 647.now by options .ok1. E(3293) = 3168 247^3168 = 1 mod 3293 247^250272 = 1 mod 3293 247 * N -1 is divisible by 3293..now by options@gautham87
Sir thanks for the inverse euler concept .. but i must say that I dont get your third step :(

149^3 N -1 = 0 mod 647 ----------------- can you pls explain this ?
5872

@grkkrg nyc apporach but i think u'v made a small mistake...js chk..wo 8/864 ki bajae 8/432 hoga...
5873
For FY-(2013-2014) TAX SYSTEM
Tax levied on an individual in percentage terms is half of the amount of absolute money earned by individual in rupees.What is the maximum money that a person can keep with himself after paying tax?
1)Rs50
2)Rs75
3)Rs25
4)Rs100
5874
@quant89 said:
@grkkrg nyc apporach but i think u'v made a small mistake...js chk..wo 8/864 ki bajae 8/432 hoga...
arre yes..
Another approach is to cross multiply:
108/1330 and 106/1284
108 * 1284 and 106 * 1330
138672 and 140980

RHS > LHS :)
5875
@19rsb 1?
5876
@19rsb said:
For FY-(2013-2014) TAX SYSTEMTax levied on an individual in percentage terms is half of the amount of absolute money earned by individual in rupees.What is the maximum money that a person can keep with himself after paying tax?1)Rs502)Rs753)Rs254)Rs100
Pata nhi kya gadbad kar raha hu :banghead:

Tax% be a
and total income be I

then a = 1/2(I - I*a/100)

Not getting the result on differentiation .. :(

5877
gudmrng puys......here's my first ques of the day.. a sitter for most.

The fraction 2/7 can be written in a unique way as the sum of two unit fractions 1/a + 1/b, where a and b are positive integers with a ??
5878
@nick_baba said:
gudmrng puys......here's my first ques of the day.. a sitter for most.The fraction 2/7 can be written in a unique way as the sum of two unit fractions 1/a + 1/b, where a and b are positive integers with a
is it 8?
5879
@19rsb said:
For FY-(2013-2014) TAX SYSTEMTax levied on an individual in percentage terms is half of the amount of absolute money earned by individual in rupees.What is the maximum money that a person can keep with himself after paying tax?1)Rs502)Rs753)Rs254)Rs100
lets take that he earns E..so he gave E/2% as tax..so he saves s=E-E/2% of E

S= E-(E/2)*E/100
for getting max. saving..lets differentiate the above wrt.E..so dS/dE is max for E=100
keeping this value of E in above eq.. we get S=50
5880
@nick_baba said:
gudmrng puys......here's my first ques of the day.. a sitter for most.The fraction 2/7 can be written in a unique way as the sum of two unit fractions 1/a + 1/b, where a and b are positive integers with a
32??