Examine the information given below and answer the questions that follow:
The letters A,B,C,D,E,F and G (not necessarily in that order) stand for seven consecutive integers from 1 to 10.
– D is three less than A.
– B is the middle term.
– F is as much less than B as C id greater than D.
– G is greater than E.
Question 1
The greatest possible value of C is how much greater than the least possible value of D?
(A) 2
(B) 3
(C) 4
(D) 5
Question 2
What will be the difference between the highest possible and lowest possible values of B?
(A) 1
(B) 3
(C) 5
(D) 7
Question 3
If A = 7, what is the sum of E and G?
(A) 8
(B) 10
(C) 12
(D) 14
Question 4
In one case, an integer X is taken. It is as much greater than C as C is greater than E. X can be written as (A + E). What will the value of D in this case?
(A) 2
(B) 3
(C) 4
(D) 5
Question 5
A is as much greater than F as which integer is less than G?
(A) A
(B) B
(C) C
(D) D
SOLUTIONS TO DAILY CSAT MISSION # 64
1. (C) 2. (B) 3. (D) 4. (A) 5. (B)
Explanations
1. Imagine if there were only two people. Then, there would only be one handshake.
When a third person joins the party, he will shake hands with both the people already at the party i.e. there will be two more handshakes. When a fourth person joins the party, he will shake hands with each of the three people already at the party i.e. there will be three more handshakes for the fourth person. This process will continue, and the number of handshakes will rise in terms of 1 + 2 + 3 + 4 + 5 + 6 + …….
105 = 1 + 2 + 3 + 4 + ……. + 14. So, for 14 handshakes to have occurred for the last person, this last person would have had to be the fifteenth person at the party.
2. The average of any two numbers always lies between the two numbers. Take any two numbers and check this.
The other options do not always lie between the two numbers.
3. To completely pass a stationary man/animal/object, train needs to cross its own entire length. When the train starts to cross, it is something like this:
When the train has crossed the man/animal/object, it looks something like this:
Look at point A. As the train has passed the stationary object, this point has moved exactly the distance ‘L’, which is the length of the train. Keep this in mind while solving any kind of question like this.
Here, in this case, their relative speeds = (60 – 30) km/hr = 30 km/hr. This means that to a person on the second train, the first train will appear to be moving at 30 km/hr, or 25/3 m/s.
Time taken is 9 seconds. In these 9 seconds, the faster train would have moved 25/3 * 9 = 75 m relative to the man on the slower train. We established earlier that this distance moved is also the length of the train. So, length of the faster train is 75 m.
4. Let the rate of simple interest be ‘r’% per annum.
Then, total interest = r% of 5000 for 3 years + r% of 12000 for 4 years i.e. 4725 = 150r + 480r , which gives r as 7.5%.
5. In one hour, the minute hand covers 360 degrees but the hour hand only covers 30 degrees. So, the minute hand gains 330 degrees over the hour hand every hour. Or, 5.5° over the hour hand every minute.
At 6 pm, the angle between the hands is 180°. In each minute, the hour hand will close down 5.5° out of this 180°. Minutes taken for the angle to reach 72° from 180° is (180 – 72)/5.5 = 19.63 minutes. This is rounded to 6:20.
After this, the angle will come down from 72° to zero after which the minute hand overtakes the hour hand, and the angle starts rising till it again reaches 72°. The total angle covered here is from -72° to 72° i.e. 144°. The time taken is 144/5.5 = 26.18 minutes. This is 19.63 + 26.18 = 45.81 minutes after 6. The rounded figure is 6:46.
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