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CAT 1993 — QA Question 48

Number TheoryEasy
Passage / Data

Directions for next 3 questions:

Q started to move from point B towards point A exactly an hour after P started from A in the opposite direction. Q’s speed was twice that of P. When P had covered one-sixth of the distance between the points A and B, Q had also covered the same distance.

The product of all integers from 1 to 100 will have the following numbers of zeros at the end.

Answer & solution

  • A

    20

  • 24

  • C

    19

  • D

    22

Solution

The number of zeros at the end will be same as the highest power of 10 in 100!.

Number of 2 in the product of all integers from 1 to 100 =1002+1004+1008+10016+10032+10064

= 50 + 25 +12 + 6 + 3 + 1= 97 and number of 5 in the product of all integers from 1 to 100 = 1005+10025 = 20 + 4 = 24.

∴ 100! = 297 × 524 × ... 
⇒ 100! = 273 × (2 × 524) × ... 
⇒ 100! = 273 × (1024) × ... 

∴ Highest power of 10 in 100! is 24.

Hence, option (b).

CAT 1993 QA Q48: The product of all integers from 1 to 100 will have the following numbers of zeros at the end. — Solution | TheCATExam