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Class Discussion: Numbers

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CAT 2025 Lesson : Class Discussion: Numbers - Divisibility: 9 to 16

Where

n

is the number of zeroes following the right-most non-zero digit of

x

!, the number of zeroes at the right for (

x

+ 4)! =

n

+ 4. What is the smallest possible value of

x

?

Answer: 621

Where

x

= 200! + 201! + 202! + 203! + 204! + 205!, how many zeroes follow the right-most non-zero digit of

x

?

Answer: 49

What are the last two digits of 1! + 2! + 3! + ... + 100! ?

Answer: 13

What are the last two digits of 282

^{282}

What is the right-most non-zero digit of 320

^{360}

+ 360

^{370}

+ 370

^{320}

?

Answer: 1

What are the last two digits of 7

^{128}

+ 9

^{64}

?

Answer: 62

In how many different ways can you pay Rs. 4,600 using notes of Rs. 2000, Rs. 500 and Rs. 200 denominations only?

How many values of

x

and

y

would satisfy

xy

x

= 12, where

x

and

y

are positive integers?

Answer: 5

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