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# Amcat model questions set - 1

1. Rahul purchased 7 DVDs each of which costs Rs.17.  He gave a five hundred rupee note to the shopkeeper.  The amount returned to him is divisible by?
A. 3
B. 7
C. 9
D. 11
Explanation:
7 DVD's cost = Rs.17×7 = Rs.119
Amount returned by the shopkeeper = 500 – 119 = 381
Checking from the options, This is divisible by 3

2. An investment earns 4 paisa per rupee invested.  If at the end of the year, the interest earned by an investment is Rs.100,then the investment is equal to?
A. 3000
B. 2500
C. 3500
D. 1500
Explanation:
Interest rate = $\dfrac{{{\rm{Interest}}}}{{{\rm{Principal}}}}{\rm{ \times 100}}$ = $\dfrac{\text{4 ps}}{\text{100 ps}}{\rm{ \times 100}}$ = 4%
Given that R% (P) = Rs.100 ⇒4%(P) = 100 ⇒P = 2500

3. The time in the clock is 8:20. What is its mirror image?
A. 3: 20
B. 3: 40:40
C. 2: 25
D. 4: 20
Explanation:
There is a simple formula to find the mirror image.  Subtract the given time from 11:60.  So mirror image = 11:60 - 8:20 = 3:40

4. In a school, for a student out of 100 he got 74 of average for 7 subjects and he got 79 marks in the 8th subject. what is the average of all the subjects?
A. 76.251
B. 80.25
C. 74.265
D. 74.625
Explanation:
Average = $\dfrac{\text{Sum of observations}}{\text{Number of observations}}$
Sum of all the marks = 74×7 + 79 = 597
Average = $\dfrac{{597}}{8}$ = 74.625

Alternative method:
In the 8th subject he additionally got 5 marks and these 8 marks are distributed to all 8 subjects equally.  Hence average  = 74 + 5/8 = 74.625

5. Amaranth told to Amanda in front of a Photo that “He is the son of my father’s son”.  Find who is in the picture if Amaranth have no brothers and sisters.
A. Amaranth himself
B.  Amaranth’s Uncle
C. Amaranth’s Father
D.  Amaranth’s son
Explanation:
Amarnath's father's son is Amarnath himself as he is the only son.  Now the photo is son of Amarnath.

6. A train travelling at 250 Km/h overtakes a cyclist who is moving at 10km/h in 45 seconds. Find the length of train in meters?
A. 3000 m
B. 5400 m
C. 6000 m
D. 10800 m
Explanation:
We know that Distance = Speed × Time.
Here Distance = Length of the train; Speed = Relative speed.
Therefore, Length of train = relative speed × time = (250 – 10) $\dfrac{5}{{18}}$ × 45 s = 3000 m

7. The Tremors of earthquake were felt at intervals of 15 seconds. The first tremor was felt at 8:54:57 and last tremor was felt at 10:45:12. How many times were the tremors felt?
A. 484
B. 485
C. 441
D. 525
Explanation:
Difference of times = 10:45:12 - 8:54:57 = 9:104:72 - 8:54:57 = 1:50 :15 = 3600 + 3000 + 15 = 6615 seconds.
Now tremors are felt at the intervals of 15 seconds.
Total = $\dfrac{{6615}}{{15}}$ = 441

8. Soha Ranks 5th in the class. How many students are there in the class?
I) One of her friends got 40th rank which is second last rank
II) Her rank is 17th from the middle

A. Statement I is alone sufficient
B. Statement II is alone sufficient
C. Both the statements put together are sufficient
D. Both the statements put together are not sufficient
E. Either of the statements are sufficient
Explanation:
Statement 1: "One of her friends got 40th rank which is second last rank"
Therefore total no of student is 40+1 = 41
Statement 2: "Her rank is 17th from the middle"
1) Soha Ranks 5th in the class
i.e. There are 4 student ahead of Soha .
2) Her rank is 17th from the middle
i.e. There are 15 students between Soha and middle student
Therefore total students on either side of middle student = 15 + 4 + 1 = 20
Total no of student = 20 (left side of middle student) + 20(right side middle student) + 1(middle student) = 41 ( student)
Hence either of the statements are sufficient.

9. A person is rock climbing at an altitude of 800 m. He go up by 7 mph. and come down by 9 mph. what was his average speed?
A. 7.875 mph
B. 7.125 mph
C. 7 mph
D. 7.5 mph
Explanation:
If distance is same in both cases, average speed = $\dfrac{\text{total distance}}{\text{Total time}}$ = $\dfrac{{2xy}}{{x+y}}$
Given that, x = 7 mph, y = 9 mph
Average speed = $\dfrac{{2 \times 7 \times 9}}{{7 + 9}}$ = 7.875 mph

10. In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?
A. 8
B. none
C. 15
D. 16