# Amcat model questions set - 2

1. What is the largest power of 20 contained in 100!?
A. 56
B. 1
C. 24
D. 2
Explanation:
20 = 5×22.
Power of 2 in 100!= $\left[ {\dfrac{{100}}{2}} \right] + \left[ {\dfrac{{100}}{4}} \right]$ + $\left[ {\dfrac{{100}}{8}} \right] + \left[ {\dfrac{{100}}{{16}}} \right]$ + $\left[ {\dfrac{{100}}{{32}}} \right] + \left[ {\dfrac{{100}}{{64}}} \right]$ = 97
Here [ ] is greatest integer function.  So only integer parts should be considered for positive numbers.
So highest power of 4 in 100! = ${\left( 2 \right)^{97}} = {\left( {{2^2}} \right)^{48}} \times 2$ = 48 times.
Highest power of 5 in 100! = $\left[ {\dfrac{{100}}{5}} \right] + \left[ {\dfrac{{100}}{{25}}} \right]$ = 24
so, Power of 20 in 100! = least of the two powers = 24

2. A seller uses 900 gm in place of 1 kg.Find his actual percentage of profit or loss when he sells his articles at 5% loss on cost price?
A. 5
B. 6
C. 5.55
D. 20
Explanation:
Let us assume one grams costs Rs.1.
He gives only 900 gm for 1 kg. So cost price = Rs.900
But he collects 5% less on the cost price.  So he collects Rs.950 from the customer. ($\because$ This
reduction should be calculated on Rs.1000 as the customer does not know about his cheating).
Profit % = $\dfrac{{50}}{{900}} \times 100$ = 5.55%

3. A coin is tossed thrice.  What is the probability that first toss of the coin lands head, second lands tail and third lands tail as well
A. 1/3
B. 1/ 6
C. 1/8
D. 1/10
Explanation:
Total ways when 3 coins are tossed = $2^3$ = 8
Now HTT is one of the way. So required probability = 1/8
Alternative method:
If a coin is tossed, getting heads or tails has the probability = 1/2
We have 3 such cases here so = 1/2 × 1/2 × 1/2 = 1/8

4. If the LCM of a and (a>b) is 667 the the value of 7b – 5a is
Explanation:
667 can be written as 29 × 23. So a = 29,  b = 23.
7b – 5a = 7×29 – 5×23 = 16

5. The money at compound interest amount to thrice it self in 16 years.  So,in how many years it will be 27 times itself ?
Explanation:
Let P be the principal.
It will thrice itself in 16 years. So it becomes = 3×P = 3P.
After another 16 years it will be 3×3P = 9P
Another after 16 years it will be 3×9P = 27P
So it will take 48 years to become 27 times.

6. INGENUITY (OPPOSITE)
A. skillfulness
B. cunning
C. inventive
D. dullness
Explanation:
Ingenuity means the quality of being original, clever.  It came from the root 'genuine' which is nobility.  So dullness can be opposite to this.

7. PRANKISH (OPPOSITE)
A. whimsical
B. Machiavellian
C. impish
D. serious

Explanation: D
Prank means childish behaviour , to put pranks on others.  So opposite to this is serious.  Machiavellian means cunning, and impish means lack of seriousness.

8. PERT (OPPOSITE)
A. impudent
B. brash
C. savvy
D. polite
Explanation:
Pert means shameless boldness.  Impudent also means the same.  Brash means the same as  impertinent, impudent.  Savvy means knowledgeable.  So Polite is opposite to pert.

9. GAUNT (OPPOSITE)
A. emaciated
B. sombre
C. plump
D. piquant