original CAT Geometry

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CAT Geometry

by Monika Bansal

Yet to come...

ystrdy my 1 stdnt came 2 me.He ws vry frustrated cz of CAT prep.He askd;"mam, wt is d usage f geometry in CAT...mera toh dabba gol hai ismein..". Thn he showed mw d following thng..


wn I saw at d figure...i laughed lyk nythng..i said;"if u want to go 2 rectangular premises of an elite B- school...u shold not be a dabba gol circle in geometry"no doubt GEOMETRY is beloved of CAT people.so,try 2 solve as many qustions as possible...nd to make it possible i m posting all d original CAT questions f d topic...Go throuh it nd enlighten ur spirits...

question on base system

(7⁷⁷)₁₀=(x)_7⁷, with how many zeroes will x end??

greatest integer fn...

if 76 < x< 92 and 142 < x< 2003; then how many solutions are possible for the following equation:
[x/143] + [2x/91] + [3x/77] = 68x/1001
where [x] represents greatest integer less than equal to x.

base sys....

A +ve integer x; (100 < x < 150); is represented in base 2, base 3, base 4 and base 5 notation. In all the 4 cases the last digits are 1, 2, 3 and 4 respectively. What will be the last digit when x is represented in base 6??

remainders..

Let p = x²⁵-x¹³+x⁶-1 ; where x>2007.
How many remainders are possible if p is divided by 7???

base sys...

Let N=2³3⁴5⁶ , How many ordered pairs (a,b) exist if h.c.f.(a,b) = 1 & a and b are factors of N??

gd 1..

I knw by adjusting 90, 91, 92, 93, 94, 95, 96 there r 7! possible numbers. How many of them are perfect square???

remainders..........

what are the remainders wn following expressions are divided by 144?
(A)1^5+2^5+3^5+....................44^5+45^5
(B)(1^5)(2^5)(3^5)....................(44^5)(45^5)
(C)1^5,2^5,3^5,....................,44^5,45^5written in a line 2get a huge no.

nd d options are
(a)zero
(b)81
(c)117
(d)45
(e)None of these

Repunit no...

if R(n) = 1111111.....111 (n times), then R(n) is known as repunit no. For how many 256 < n < 343, R(n) will be perfect square???

last two digits...

a.) 135^251

b.) 145^260

c.)165^266

factors...

how many natural nos. between 1 and 100 have exactly 4 factors??

find d remainder...

***remainder when 141414141........1414 (404 digits) is divided by 909??
(a) 9
(b)303
(c)101
(d)505
(e) none of these

last two digits..

what are the last two digits of 9 raise to power 9 raise to power 9?

last 2 places ...

*** last two places of 399^43???

last two digits...

*** What are d last 2 digits of 36! - 24! ???

question on HCF......

****N=21600, how many pairs (a,b) exist such that a & b are factors of N and hcf (a,b) = 45???

Tale from Harvard Business Review

A Red Indian walks into a cafe with a shotgun in one hand and a bucketof buffalo manure in the other.
He says to the waiter, "Me want coffee."

The waiter says, "Sure chief, comin right up."

He gets the Indian a tall mug of coffee, and the Indian drinks it downin one gulp, picks up the bucket of manure, throws it intothe air,blasts it with the shotgun, then just walks out.

The next morning the Indian returns. He has his shotgun in one hand anda bucket of buffalo manure in the other. He walks up to thecounter andsays to the waiter, "Me want coffee."
The waiter says, "Whoa, Tonto! We're still cleaning up your mess fromyesterday. What the heck was all that about, anyway?"

The Indian smiles and proudly says, "Me training for uppermanagementposition:
Come in,
drink coffee,
shoot some crap,
leave mess forothers to clean up,
disappear for rest of day." : )))

Perfect Nos' Properties.....contd.

5. The even perfect numbers' final digits would go either 6 or 8.
6. Every even perfect no. is a triangular no.
7. Every even perfect no. can be written as sum of cubes of consecutive odd nos.

Some properties of perfect nos...

1. sum of reciprocals of all d divisors of a perfect no. is always 2.
2. Every even perfect no. can be written as 2^x-1(2^x-1), where 2^x-1 is a prime.
3. First 4 perfect nos. are 6, 28, 496 and 8128.
6=2^2-1(2²-1)
28=2^3-1(2³-1)
496=2^5-1(2⁵-1)
8128=2^7-1(2⁷-1)
4. Till d date, there is no known odd perfect no.It does not mean that thr is not any odd perfect no.