Official Quant thread for CAT 2013

@abhishek.2011 said:
sum till 1 to 9 = 45so 45*4+10+20+30+4=244244/9 rem = 1
correct answer..

Better approach:

for 1 digit nos:
since 10 mod 9=1 so we can take 1+2+3+4+5+6+7+8+9

for 2 digit nos:
since 100 mod 9=1 so we can take 10+11+12+13+14......

same for 3 digit or n digit nos (if it would have been beyond 40)

so its nothing but sum of all natural nos till 40.. rest u know..
@jain4444 said:
A went on a tour. He visited a total of 8 cities. In each city he spent Rs.2 less than half the amount he had with him. He spent Rs.100 in the last city he visited. Find the amount he had initially (in Rs.)?
Edit: Calc error!
It is coming out to be 26620

@jain4444 said:
A went on a tour. He visited a total of 8 cities. In each city he spent Rs.2 less than half the amount he had with him. He spent Rs.100 in the last city he visited. Find the amount he had initially (in Rs.)?
26620?
@jain4444 said:
A went on a tour. He visited a total of 8 cities. In each city he spent Rs.2 less than half the amount he had with him. He spent Rs.100 in the last city he visited. Find the amount he had initially (in Rs.)?
@viewpt said:
25604??
@ChirpiBird said:
26620?
@Dexian said:
2060???
@amresh_maverick said:
26620
@ScareCrow28 said:
Edit: Calc error!It is coming out to be 26620

its 25604

100 = (x/2) - 2
204 = (x/2) + 2
404 = (x/2) + 2
804 = (x/2) + 2
1604 = (x/2) + 2
3204 = (x/2) + 2
6404 = (x/2) + 2
12804 = (x/2) + 2
25604 = initially

arey mera answer 2060.......... wo AP series wale ka tha.........@amresh_maverick sir ke question ka........

@jain4444 said:
its 25604 100 = (x/2) - 2 204 = (x/2) + 2 404 = (x/2) + 2 804 = (x/2) + 2 1604 = (x/2) + 2 3204 = (x/2) + 2 6404 = (x/2) + 2 12804 = (x/2) + 2 25604 = initially
Sir, Acc to you he had 25604 initially, so he must have spent 25604/2 - 2 = 12802 - 2= 12800 in the 1st city whereas he has spent 12804 acc to you.. anomaly?
Aur ek me "-" use hua aur bakiyo me "+" ?? I couldn't get the solution..
@Dexian said:
arey mera answer 2060.......... wo AP series wale ka tha.........@amresh_maverick sir ke question ka........
There a link to "Quote" at bottom right corner of a post. Please use that for quoting someone otherwise it creates confusion.
@ScareCrow28 said:
Sir, Acc to you he had 25604 initially, so he must have spent 25604/2 - 2 = 12802 - 2= 12800 in the 1st city whereas he has spent 12804 acc to you.. anomaly?
bhai sir na bolo yaar

he spent = 100 at last city

100 = (x/2) - 2
=> x = 204

now 204 is the amount which he had at 7th city after spending some amount there so this amount is nothing but half + 2 of the amount which he had at 6th after spending and so on


@ScareCrow28 said:
Sir, Acc to you he had 25604 initially, so he must have spent 25604/2 - 2 = 12802 - 2= 12800 in the 1st city whereas he has spent 12804 acc to you.. anomaly?

@jain4444 said:
its 25604 100 = (x/2) - 2 204 = (x/2) + 2 404 = (x/2) + 2 804 = (x/2) + 2 1604 = (x/2) + 2 3204 = (x/2) + 2 6404 = (x/2) + 2 12804 = (x/2) + 2 25604 = initially


true that.
everytime the left amount is halved then 2 is subtracted.

so 1st city he spends.. X/2-2
next he spends (X-4)/4 -2 ... and so on..

@amresh_maverick
wat is the OA for that AP series sum..........
2060??
@jain4444 said:

its 25604

100 = (x/2) - 2
204 = (x/2) + 2
404 = (x/2) + 2
804 = (x/2) + 2
1604 = (x/2) + 2
3204 = (x/2) + 2
6404 = (x/2) + 2
12804 = (x/2) + 2
25604 = initially

m too getting 25604
everytime spending is
x-4/2^n
where n is no of city visited
for n=8
x-4/256=100
x=25604
@jain4444 said:
bhai sir na bolo yaar he spent = 100 at last city 100 = (x/2) - 2 => x = 204 now 204 is the amount which he had at 7th city after spending some amount there so this amount is nothing but half + 2 of the amount which he had at 6th after spending and so on
Aahhhh... Got it!
@ChirpiBird said:
true that. everytime the left amount is halved then 2 is subtracted.so 1st city he spends.. X/2-2 next he spends (X-4)/4 -2 ... and so on..
we need to concentrate on the amount that he has left with after spending some amount on a particular city except last city


@abhishek.2011 said:
37^64/100split 100 in 25*4euler of 4 = 2 64/2=0 so rem of 37^64/4=1euler of 25 = 4*25/5=2064/20=437^4/25=11so only 61 satisfies
@ChirpiBird said:
(37*37)^32 = .. {(1369)(1369)}^16= (61)^16= 61 last two digits..
correct answer ...

Better approach:

Last two digit for 37^64
=(37^4)^16 {Cyclicity of 7 is 4}
=(37^2*37^2)^16
=(13^2*13^2)^16
=(69*69)^16
=(19*19)^16
=(61)^16
=61

can be done just in mind too..

@jain4444 said:
bhai sir na bolo yaar he spent = 100 at last city 100 = (x/2) - 2 => x = 204 now 204 is the amount which he had at 7th city after spending some amount there so this amount is nothing but half + 2 of the amount which he had at 6th after spending and so on
last city he will spend {(X-508)/256}-2 and this is equal to 100.
@jain4444 said:
we need to concentrate on the amount that he has left with after spending some amount on a particular city except last city
ohkkk..
@ChirpiBird said:
find the 60th digit after decimal in the expansion of 1/2013 ...
Mera doubt bhi clear karo please..
kindly post the method too..
@ScareCrow28 said:
Ways if 1 woman holds VP/P = 4C3*3C1*4C2*2*24C3 --- Taking 3 females of 4 3C1 --- Taking 1 lady of those 3 and assigning some position ( P/VP)4C2 --- Taking 2 Males2 ------ Ways of assigning a post to a female2 ------ Ways of assigning a post to two malesSimilarly others have been realised. Hope you can make out others too. Sorry for late reply.
Thank you for your explanation.:)

If 2 women hold P/VP position = 4C4*4C1*3*4 = 48

I can't understand that particular step. What do 3 and 4 represent? And also, is it not necessary to divide everything by 3!, because of the three secretary jobs?


p,q,r are non negative integers such that p + q + r = 10 the maximum value of pqr + pr + qr + pq is
a- >=40 and
b- >=50 and
c- >=60 and
d- >=70 and
e- >=80 and

dunno the oa. plz post ur approach.
@Sybar said:
Thank you for your explanation.If 2 women hold P/VP position = 4C4*4C1*3*4 = 48I can't understand that particular step. What do 3 and 4 represent? And also, is it not necessary to divide everything by 3!, because of the three secretary jobs?
If 2 women hold P/VP position = 4C4*4C1*3*4 = 48
4C4 --- Take 4 Females of 4
4C1 --- Take 1 Male of 4
Now, the male has 1 place to go to. ( Any of 3 secretaries )
And Take any 2 females in 4C2 ways which can be arranged in 2! ways or 4P2 ways = 3*4
Sorry for directly writing the values 😞 and being late in reply ( SBI PO form ni bhar par )