Quant Question of the Day Chat

I am not sure if its 1 looking at the the option would be really great

There is a pattern like this

36^2 = ...96
36^3 = ...76
36^4 = ...56
36^5 = ...36
36^6 = ...16
Repeat after this same pattern
36^7 = ...96

So the last 2 digits are now easy to calculate ..

I.e divide the powers 55 by 5 and from the remainder you will get in which range the last 2 digits fall

Do the same for the power 41

Last 2 digits we will get

But still we need the options to know wheather it’s 1 or 6 or something else

PS: Correct me if I am wrong

Dividing by 55 can have remainders in range of 1 - 54 so looking at options will help us solve this faster, but if we need exact answer then there can be some other method, which I would be interested in knowing

Why cyclicity concept will be used here for remainder? For specific divisors we will use ryt.. plz correct me

If you dont want to use this use binomial expansion for the actual amswer

No m asking can we use cyclicity rule here ?

1. Using cyclicity rule we can zero in on the options but if multiple choices match we can’t be use like if both 1 and 6 were there in the ans I would have used Binomial expansion
2. 6 is the answer not 1

Binomial expansion was equally fast

Can u share me some of the link or anything where I can refer to calculate such qs using binomial expansion. I only know when we can expand the dividend in some form of (a-1)^n ..

Expand it as (11 + 5²)^55^41

Now only 1st term of binomial will contain power of 11 and last term power of 5 rest all terns will have mixed powers of 11 and 5 making them multiple of 55

C⁰.11⁵⁵*⁴¹.5⁰ + ( here all mixed terms are multiples ) + C⁵⁵*⁴¹.11⁰.5²*⁵⁵*⁴¹

Thus we are looking at reduced terms

11⁵⁵*⁴¹ / 55 ( now ofcourse it will factor out 11 remaining to check for divisiblity by 5 and you know remainder will be 1 cuz 11^anything will have 1 in last digit )
besides you can again use BT as (10 + 1)⁵⁵*41 / 55

+

(5¹¹⁰)^41 / 55
or
5⁴⁵⁰⁹ / 11
(this is a bit tricky part , but remainder of this is 0)
expand it using (11 - 1)⁴⁵⁰⁹ / 22 use binomial expansion and again find out which terms are multiples of 22
This specific part can also be calculated using modular arithmetic( refer geekforgeeks )

So total remainder 1 + 0 = 1

Binomial theorem: https://byjus.com/jee/binomial-theorem/

Correction: 1 is the remainder

Ranu2024

A right circular cylinder with radius 6 units and height 10 units is placed upright and is filled up to 2/5th of its volume with water. a solid cone of radius 3 units and height 4 units is then submerged completely in the cylinder. What is the increase in the height of water level ? - Can someone solve this ?

yes correct

can you send the solution ?

Volume of cone = 12π ..using 1/3πr^2
Now this is submerged in cylinder...so 12π = π (6)^2 * H ( using volume of cylinder formula) and H is height required

Hey Guys, I am sharing a pdf of Jamboree’s Advanced Level Questions (Topic: Geometry). Can someone solve and share the solution booklet for the same ? I couldn’t find solutions for these questions on the GMAT Club or anywhere else.

Why you guys reading Geometry when it wont come from January in GMAT. Are you planning to give exam in 1-2 months?

Which B school will accept the score if I will take GMAT in 1-2 month

ISB
SPJIMR
XIM B

MICA too

IMT

are you giving focus edition?

I am planning to give focus edition as I started preparing from 15 days, so till I prepare the older GMAT wont be valid, so planning to prepare for focus

A slew of people are going to sot for the classic tests, so they need to practice Geometry