1.  All of the students at a college are majoring in psychology, business, or both. 73% of the students are psychology majors, & 62% are business majors. If there are 200 students, how many of them are majoring in both psychology & business?

Answer :

70 students are majoring in both, psychology & business

If 73% of the students are psychology majors, we know that 27% are not psychology majors. By the same reasoning, 38% are not business majors, because 62% of the students do major in business. So: 27 + 38 = 65

65% of the students are not majoring in both psychology & business, so 35% are double majors, a total of 70 students.

2.  Thus, Mr. Haani must have crossed 7 SlowRun Expresses during his journey.

Six cabins numbered 1-6 consecutively, are arranged in a row and are separated by thin dividers. These cabins must be assigned to six staff members based on following facts.

Miss Shalaka's work requires her to speak on the phone frequently throughout the day.

Miss Shudha prefers cabin number 5 as 5 is her lucky number.

Mr. Shaan and Mr. Sharma often talk to each other during their work and prefers to have adjacent cabins.

Mr. Sinha, Mr. Shaan and Mr. Solanki all smoke. Miss Shudha is allergic to smoke and must have non-smokers adjacent to her.

Mr. Solanki needs silence during work.

Can you tell the cabin numbers of each of them?

Answer :

The cabins from left to right (1-6) are of Mr. Solanki, Mr. Sinha, Mr. Shaan, Mr. Sharma, Miss Shudha and Miss Shalaka.

From (2), cabin number 5 is assigned to Miss Shudha.

As Miss Shudha is allergic to smoke and Mr. Sinha, Mr. Shaan & Mr. Solanki all smoke, they must be in cabin numbers 1, 2 and 3 not necessarily in the same order. Also, Miss Shalaka and Mr. Sharma must be in cabin 4 and 6.

From (3), Mr. Shaan must be in cabin 3 and Mr. Sharma must be in cabin 4. Thus, Miss Shalaka is in cabin 6.

As Mr. Solanki needs silence during work and Mr. Shaan is in cabin 3 who often talks to Mr. Sharma during work, Mr. Solanki must be in cabin 1. Hence, Mr. Sinha is in cabin 2.

Thus, the cabins numbers are
1# Mr. Solanki,
2# Mr. Sinha,
3# Mr. Shaan,
4# Mr. Sharma,
5# Miss Shudha,
6# Miss Shalaka

3. SkyFi city is served by 6 subway lines - A, E, I, O, U and Z.

When it snows, morning service on line E is delayed.

When it rains or snows, service on the lines A, U and Z is delayed both morning and afternoon.

When the temperature drops below 20 C, afternoon service is cancelled on either line A or line O, but not both.

When the temperature rises above 40 C, afternoon service is cancelled on either line I or line Z, but not both.

When service on line A is delayed or cancelled, service on line I is also delayed.

When service on line Z is delayed or cancelled, service on line E is also delayed.

On February 10, it snows all day with the temperature at 18C. On how many lines service will be delayed or cancelled, including both morning and afternoon?

SkyFi city is served by 6 subway lines - A, E, I, O, U and Z.

When it snows, morning service on line E is delayed.

When it rains or snows, service on the lines A, U and Z is delayed both morning and afternoon.

When the temperature drops below 20 C, afternoon service is cancelled on either line A or line O, but not both.

When the temperature rises above 40 C, afternoon service is cancelled on either line I or line Z, but not both.

When service on line A is delayed or cancelled, service on line I is also delayed.

When service on line Z is delayed or cancelled, service on line E is also delayed.

On February 10, it snows all day with the temperature at 18C. On how many lines service will be delayed or cancelled, including both morning and afternoon?

In a certain game, if 2 wixsomes are worth 3 changs, and 4 changs are worth 1 plut, then 6 plutes are worth how many wixsomes?

Answer :

It is given that
2 wixsomes = 3 changs
8 wixsomes = 12 changs ----- (I)

Also, given that
4 changs = 1 plut
12 changs = 3 plutes
8 wixsomes = 3 plutes ----- From (I)

Therefore,
6 plutes = 16 wixsomes

4. You have four 9's and you may use any of the (+, -, /, *) as many times as you like. I want to see a mathematical expression which uses the four 9's to = 100     How many such expressions can you make?

Answer :     There are 5 such expressions.

99 + (9/9) = 100

(99/.99) = 100

(9/.9) * (9/.9) = 100

((9*9) + 9)/.9 = 100

(99-9)/.9 = 100

5.  There is a 50m long army platoon marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position.In the mean time the whole platoon has moved ahead by 50m.The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.

Answer :     The last person covered 120.71 meters.

It is given that the platoon and the last person moved with uniform speed. Also, they both moved for the identical amount of time. Hence, the ratio of the distance they covered - while person moving forward and backword - are equal.

Let's assume that when the last person reached the first person, the platoon moved X meters forward.

Thus, while moving forward the last person moved (50+X) meters whereas the platoon moved X meters.

Similarly, while moving back the last person moved [50-(50-X)] X meters whereas the platoon moved (50-X) meters.

Now, as the ratios are equal,
(50+X)/X = X/(50-X)
(50+X)*(50-X) = X*X

Solving, X=35.355 meters

Thus, total distance covered by the last person
= (50+X) + X
= 2*X + 50
= 2*(35.355) + 50
= 120.71 meters

Note that at first glance, one might think that the total distance covered by the last person is 100 meters, as he ran the total length of the platoon (50 meters) twice. TRUE, but that's the relative distance covered by the last person i.e. assuming that the platoon is stationary.

6. Mr. Subramaniam rents a private car for Andheri-Colaba-Andheri trip. It costs him Rs. 300 everyday.

One day the car driver informed Mr. Subramaniam that there were two students from Bandra who wished to go from Bandra to Colaba and back to Bandra. Bandra is halfway between Andheri and Colaba. Mr. Subramaniam asked the driver to let the students travel with him.

On the first day when they came, Mr. Subramaniam said, "If you tell me the mathematically correct price you should pay individually for your portion of the trip, I will let you travel for free."

How much should the individual student pay for their journey?

Answer :

The individual student should pay Rs. 50 for their journey.

Note that 3 persons are travelling between Bandra and Colaba.

The entire trip costs Rs. 300 to Mr. Subramanian. Hence, half of the trip costs Rs. 150.

For Andheri-Bandra-Andheri, only one person i.e. Mr. Subramaniam is travelling. Hence, he would pay Rs. 150.

For Bandra-Colaba-Bandra, three persons i.e Mr. Subramaniam and two students, are travelling. Hence, each student would pay Rs. 50.

7. The cricket match between India and Pakistan was over.

Harbhajan scored more runs than Ganguly.

Sachin scored more runs than Laxman but less than Dravid

Badani scored as much runs as Agarkar but less than Dravid and more than Sachin.

Ganguly scored more runs than either Agarkar or Dravid.

Each batsman scored 10 runs more than his immediate batsman. The lowest score was 10 runs. How much did each one of them score

Answer :

A simple one. Use the given facts and put down all the players in order. The order is as follow with Harbhajan, the highest scorer and Laxman, the lowest scorer.

Harbhajan

Ganguly

Dravid

Badani, Agarkar

Sachin

Laxman

Also, as the lowest score was 10 runs. Laxman must have scored 10, Sachin 20, Badani & Agarkar 30 and so on.

Harbhajan - 60 runs

Ganguly - 50 runs

Dravid - 40 runs

Badani, Agarkar - 30 runs each

Sachin - 20 runs

Laxman - 10 runs

8. At what time immediately prior to Six O'clock the hands of the clock are exactly opposite to each other. Give the exact time in hours, minutes and seconds

Answer :

It is obvious that between 5 O'clock and 6 O'clock the hands will not be exactly opposite to each other. It is also obvious that the hands will be opposite to each other just before 5 O'clock. Now to find exact time:

The hour hand moves 1 degree for every 12 degrees that the minute hand moves. Let the hour hand be X degree away from 5 O'clock. Therefore the minute hand is 12X degree away from 12 O'clock.

Therefore solving for X

Angle between minute hand and 12 O'clock + Angle between 12 O'clock and 4 O'clock + Angle between 4 O'clock and hour hand = 180
12X + 120 + (30-X) = 180
11X = 30
Hence X = 30/11 degrees
(hour hand is X degree away from 5 O'clock)

Now each degree the hour hand moves is 2 minutes.

Therefore minutes are
= 2 * 30/11
= 60/11
= 5.45 (means 5 minutes 27.16 seconds)

Therefore the exact time at which the hands are opposite to each other is
= 4 hrs. 54 min. 32.74 seconds

9. The minute and the hour hand of a watch meet every 65 minutes. How much does the watch lose or gain time and by how much?

Answer :

The minute and the hour hand meet 11 times in 12 hours in normal watch i.e. they meet after every
= (12 * 60) / 11 minutes
= 65.45 minutes
= 65 minutes 27.16 seconds

But in our case they meet after every 65 minutes means the watch is gaining 27.16 seconds.

10. A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now his salary is Rs. 22702.68      What was his salary to begin with?

Answer :      Rs.22176

Assume his salary was Rs. X

He earns 5% raise. So his salary is (105*X)/100

A year later he receives 2.5% cut. So his salary is ((105*X)/100)*(97.5/100) which is Rs. 22702.68

Hence, solving equation ((105*X)/100)*(97.5/100) = 22702.68
X = 22176