1) You have a total of 10 questions to be attempted in 15 minutes.
2) There is only one correct answer for each question.
3) 4 marks will be awarded for each right answer and 1 mark will be deducted for each wrong answer.
4) You have an option to skip a question without any penalty.
5) At the end of the test you can see a detailed feedback on each question.
Question 1.
A company manufactures pencils in boxes of 6, 9, and 20. The boxes are sealed and the pencils cannot be sold loose. What is the largest number of pencils that a wholesaler cannot purchase using some combination of these boxes? 43 199 99 86 None of these Skip this question |
Question 2.
Consider 4 (dimensionless) flies, 2 males and 2 females. They are situated at the four corners of a square of side 10 meters, the two males at diagonally opposite ends. At any time, each fly tries to reach the male-female fly in front of her-him using the shortest possible route. Since the flies are flying towards another, they will meet each other at a certain time at the center of the square. What is the length of the path that each has traveled at the moment they reach each other? 12.5 mts 10 mts 7.5 mts 5 mts None of these Skip this question |
Question 3.
A man is going to a car auction. All purchases must be paid for in cash. He goes to the bank and draws out Rs. 25,000. Since the man does not want to be seen carrying that much money, he places it in 15 envelopes numbered 1 through 15 such that he could count any amount from 1 to 25000 using combinations of some envelopes. Each envelope contains the least number of bills possible of any available currency. (for example, no two tens instead of a twenty). The possible currency denominations are 1,2,5,10, 20, 50 and 100. At the auction he makes a successful bid of Rs. 8322 for a car. He hands the auctioneer envelopes 2, 8, and 14. After opening the envelopes the auctioneer finds exactly the right amount. How many ones (one rupee notes) did the auctioneer find in the envelopes. 1 2 3 4 None of these Skip this question |
Question 4.
A traveler, on his way to a certain village A, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to village A, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions. The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies. With which of the following questions can the traveler find out the way to village A by asking just this one question to one of the two brothers? Does the left road lead to village A according to your brother? Which road leads to village A according to your brother? If I were to take the left road then what according to your brother will be the answer to the question Am I on the right road ? Does the right road lead to village A according to your brother? None of these Skip this question |
Question 5.
On Madagascar Island, there are x dodos in a particular year. 30 dodos in a thousand of the original population die every year and 25 dodos in a thousand of the original population are born every year. In how many years will the population of dodos halve itself ? 200 125 100 50 None of these Skip this question |
Question 6.
A cube is divided into 8 equal cubes. Each of these cubes is further sub-divided into 8 equal cubes. If the original cubes sides are painted blue, then what is the probability that exactly 2 sides of a small cube is painted blue ? 3/8 1/16 1/4 3/4 None of these Skip this question |
Question 7.
Balancing cards on one another where some are placed horizontally and others diagonally (slant fashion) is a popular trick of all magicians. 30 playing cards of length 12 cm and breadth 6 cm are used to build a pyramidal structure with 4 horizontal cards at the base. 8 cards are then put diagonally on these cards to give four peaks. 3 cards are then put on the 4 peaks. The process continues till the top is a peak made by 2 cards. Find the area covered by the front side of the pyramid. 288 sqrt(3) cm2 180 sqrt(3) cm2 360 sqrt(3) cm2 576 sqrt(3) cm2 None of these Skip this question |
Question 8.
A man buys shares at a discount of Rs.x. Later he sells all but 10 of the shares he purchased at a premium of Rs.x. If his investment was Rs.4500 and proceeds from the sale were Rs.6250, how many shares did he buy originally ? [Assume face value of shares as Rs.100.] 50 40 60 90 None of these Skip this question |
Question 9.
ABCD is a rectangle with AB = 6 cm and AD = 8 cm. QR is an arc which cuts the extension of AD at Q and AB at R. What is the length of the arc QR if C is a point on it ? 10 pie 5 pie 20 pie 24 pie None of these Skip this question |
Question 10.
The diameter of the smaller circle is equal to the side of the square and the diagonal of the square is equal to the diameter of the bigger circle. If the circles are concentric, then their areas are in the ratio. 1:2 2:3 1:sqrt(2) 1:4 None of these Skip this question |
Answers
Question 1
A company manufactures pencils in boxes of 6, 9, and 20. The boxes are sealed and the pencils cannot be sold loose. What is the largest number of pencils that a wholesaler cannot purchase using some combination of these boxes?
1. 43
2. 199
3. 99
4. 86
5. None of these
Explanation
With combinations of 6 and 9, all multiples of 3 starting from 6 upto infinity can be purchased. With combination of one 20 box, and then some combinations of 6 and 9, all values which are 1 less than any multiple of 3, starting from 26 to infinity, can be purchased. With combination of two 20 boxes, and then some combinations of 6 and 9, all values which are 2 less than any multiple of 3, starting from 46 to infinity, can be purchased. -Now we can purchase multiples of 3, 1 less than multiple of 3 and 2 less the multiple of 3. Now 3 less than a multiple of 3 would anyway be a multiple of 3. So we have all numbers starting from 46 covered. 45 is a multiple of 3. So counted in 1st step. 44 is 1 less than a multiple of 3, so counted in 2nd step. 43 is not counted. So answer = 43. Shortcut: For better visualization of the above, answer the question “What is the largest number that cannot be created using some combination of 2 and 5. Answer is obviously 3.
Question 2
Consider 4 (dimensionless) flies, 2 males and 2 females. They are situated at the four corners of a square of side 10 meters, the two males at diagonally opposite ends. At any time, each fly tries to reach the male-female fly in front of her-him using the shortest possible route. Since the flies are flying towards another, they will meet each other at a certain time at the center of the square. What is the length of the path that each has traveled at the moment they reach each other?
1. 12.5 mts
2. 10 mts
3. 7.5 mts
4. 5 mts
5. None of these
Explanation
Because all flies constantly fly perpendicular to another fly, they all travel the shortest distance to each other, which is 10 meter. All flies make a kind of spiral flight to the center of the square, and during this flight, the flies constantly form a square until they meet in the center. The flies all travel 10 meter
Question 3
A man is going to a car auction. All purchases must be paid for in cash. He goes to the bank and draws out Rs. 25,000. Since the man does not want to be seen carrying that much money, he places it in 15 envelopes numbered 1 through 15 such that he could count any amount from 1 to 25000 using combinations of some envelopes. Each envelope contains the least number of bills possible of any available currency. (for example, no two tens instead of a twenty). The possible currency denominations are 1,2,5,10, 20, 50 and 100. At the auction he makes a successful bid of Rs. 8322 for a car. He hands the auctioneer envelopes 2, 8, and 14. After opening the envelopes the auctioneer finds exactly the right amount. How many ones (one rupee notes) did the auctioneer find in the envelopes.
1. 1
2. 2
3. 3
4. 4
5. None of these
Explanation
He has to put the numbers 2. i.e. 1,2,4,8,16,32... you can count any numbers till 2n-1 using this.
All money amounts in the envelopes are 2 (number of envelope - 1).
In Envelope #14, there are: 81 Rs.100 bills = Rs.8100 , 1 Rs. 50 bill = Rs. 50, 2 Rs. 20 bills = Rs. 40, 1 Rs. 2 bill = Rs. 2 ----- + Rs.8192 (total amount of money for Envelope #14)
In Envelope #8, there are: 1 Rs.100 bill = Rs.100, 1 Rs. 20 bill = Rs. 20, 1 Rs. 5 bill = Rs. 5, 1 Rs. 2 bill = Rs. 2, 1 Rs. 1 bill = Rs. 1 <- that's the one! ---- Rs.128 (total amount of money for Envelope #8)
Envelope #2 has 1 Rs.2 bill in it, which is its total amount also. Now Rs.8192 + Rs.128 + Rs.2 = Rs.8322. And that is the winning bid!
Hence, there are no one ruppee notes given to the autioneer. Hence (5) is the correct answer.
Question 4
A traveler, on his way to a certain village A, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to village A, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions. The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies. With which of the following questions can the traveler find out the way to village A by asking just this one question to one of the two brothers?
1. Does the left road lead to village A according to your brother?
2. Which road leads to village A according to your brother?
3. If I were to take the left road then what according to your brother will be the answer to the question Am I on the right road ?
4. Does the right road lead to village A according to your brother?
5. None of these
Explanation
There are four possible cases: The traveler asks the question to the truth-telling brother, and the left road leads to village A. The truth-telling brother knows that his lying brother would say that the left road does not lead to village A, and so he answers No. The traveler asks the question to the truth-telling brother, and the right road leads to village A. The truth-telling brother knows that his lying brother would say that the left road leads to village A, and so he answers Yes. The traveler asks the question to the lying brother, and the left road leads to village A. The lying brother knows that his truth-telling brother would say that the left road leads to village A, and so he lies No. The traveler asks the question to the lying brother, and the right road leads to village A. The lying brother knows that his truth-telling brother would say that the left road does not lead to village A, and so he lies Yes. Hence [1]
Question 5
On Madagascar Island, there are x dodos in a particular year. 30 dodos in a thousand of the original population die every year and 25 dodos in a thousand of the original population are born every year. In how many years will the population of dodos halve itself ?
1. 200
2. 125
3. 100
4. 50
5. None of these
Explanation
Every year 5 in a thousand, i.e. 0.5% of the dodos are eliminated from the population. In 100 years, 50% of the population will be eliminated.
Question 6
A cube is divided into 8 equal cubes. Each of these cubes is further sub-divided into 8 equal cubes. If the original cubes sides are painted blue, then what is the probability that exactly 2 sides of a small cube is painted blue ?
1. 3/8
2. 1/16
3. 1/4
4. 3/4
5. None of these
Explanation
Out of 64 cubes, 24 are painted 2 on the exactly two sides. Hence ratio = 3/8.
Question 7
Balancing cards on one another where some are placed horizontally and others diagonally (slant fashion) is a popular trick of all magicians. 30 playing cards of length 12 cm and breadth 6 cm are used to build a pyramidal structure with 4 horizontal cards at the base. 8 cards are then put diagonally on these cards to give four peaks. 3 cards are then put on the 4 peaks. The process continues till the top is a peak made by 2 cards. Find the area covered by the front side of the pyramid.
1. 288 sqrt(3) cm2
2. 180 sqrt(3) cm2
3. 360 sqrt(3) cm2
4. 576 sqrt(3) cm2
5. None of these
Explanation
Area of one triangle = sqrt(3)/4 × 12 × 12 = 36 sqrt(3) cm2. Total area = 16 × 36 sqrt(3) = 576 sqrt(3) cm2.
Question 8
A man buys shares at a discount of Rs.x. Later he sells all but 10 of the shares he purchased at a premium of Rs.x. If his investment was Rs.4500 and proceeds from the sale were Rs.6250, how many shares did he buy originally ? [Assume face value of shares as Rs.100.]
1. 50
2. 40
3. 60
4. 90
5. None of these
Explanation
Let the man buy z shares. z(100 – x) = 4500 and (z – 10)(100 + x) = 6250. Solving we get z = 60.
Question 9
ABCD is a rectangle with AB = 6 cm and AD = 8 cm. QR is an arc which cuts the extension of AD at Q and AB at R. What is the length of the arc QR if C is a point on it ?
1. 10 pie
2. 5 pie
3. 20 pie
4. 24 pie
5. None of these
Explanation
If AB = 6 and AD = 8, then BC = sqrt(8^2 + 6^2) = 10 QR is 1/4th of the circumference of a circle whose centre is A. Hence, QR = 20 pie/4 = 5 pie
Question 10
The diameter of the smaller circle is equal to the side of the square and the diagonal of the square is equal to the diameter of the bigger circle. If the circles are concentric, then their areas are in the ratio.
1. 1:2
2. 2:3
3. 1:sqrt(2)
4. 1:4
5. None of these
Explanation
Area of smaller circle =pie a^2. Area of bigger circle = pie(asqrt(2))^2 = 2piea^2. Ratio of their areas = 1 : 2.
Posts
0 comments:
Post a Comment