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math & puzzles Online Quiz - 55

Description: math & puzzles Online Quiz - 55
Number of Questions: 20
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Tags: math & puzzles
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A sequence 192, 360, 576……. is formed by multiplying the corresponding terms of two different Arithmetic Progressions. What is the eighth term of the sequence?

  1. 2376

  2. 1040

  3. 2116

  4. None of these


Correct Option: A

AI Explanation

To find the eighth term of the sequence, we need to determine the common difference of both Arithmetic Progressions (APs) being multiplied.

Let's assume the first AP has a common difference of 'd1' and the second AP has a common difference of 'd2'.

The first term of the sequence is given as 192, which can be written as the product of the first terms of both APs: 192 = (a1 + d1) * (a1 + d2)

Similarly, the second term of the sequence is given as 360, which can be written as: 360 = (a1 + 2d1) * (a1 + 2d2)

To find the common differences 'd1' and 'd2', we can solve these two equations simultaneously. Subtracting the first equation from the second equation, we have: 360 - 192 = (a1 + 2d1) * (a1 + 2d2) - (a1 + d1) * (a1 + d2) 168 = a1 * d2 + a1 * 2d2 + 2d1 * a1 + 2d1 * 2d2 - a1 * d1 - d1 * d2

Since the product of two APs is also an AP, we can assume that the product of the common differences 'd1' and 'd2' is also an AP with a common difference 'd'. Therefore, we can rewrite the equation as: 168 = 2a1 * d + 2d^2

Simplifying the equation, we have: 2d^2 + 2a1 * d - 168 = 0

We can solve this quadratic equation to find the value of 'd'. Once we have 'd', we can find the eighth term of the sequence by multiplying the corresponding eighth terms of the two APs.

Since the options provided do not include the values of 'a1' and 'd', we cannot determine the exact value of the eighth term. Therefore, the correct answer is D) None of these.

A two digit number is divided by the sum of its digits. What is the maximum possible remainder?

  1. 13

  2. 14

  3. 15

  4. 16


Correct Option: C

News Reporter: There are rumours that Prime Minister Manmohan Singh will reshuffle his cabinet in the next few days. But, all the previous reshuffles took place only after a high level meeting between Prime Minister Manmohan Singh and UPA Chairperson Mrs. Sonia Gandhi. No such meeting has occurred or is planned. Therefore, the rumours are false. Which of the following most clearly states the logical flaw in the argument?

  1. The news reporter has mistakenly considered the mandatory condition as a sufficient condition and has based his/her conclusion on that.

  2. The news reporter, instead of providing adequate support to his conclusion, concludes on the basis of popular perception.

  3. The news reporter assumes if one event leads to another, then if the first does not take place it would mean that the second event would also not happen.

  4. The news reporter takes for granted that a high level meeting between the PM and the UPA chairperson is a desirable precursor of any cabinet reshuffle


Correct Option: C

A. Even to suggest, in the recent climate, that an artwork might be good because it is pleasurable, as opposed to cognitively, morally or politically beneficial, is to court derision. B. Much of the discourse about beauty since the Eighteenth century had deployed a notion of the ‘aesthetic’, and so that notion in particular came in for criticism. C. The twentieth century has not been kind to the notions of beauty or the aesthetic. D. This disdain for the aesthetic may have roots in a broader cultural Puritanism, which fears the connection between the aesthetic and pleasure.

  1. BCAD

  2. BDAC

  3. BDCA

  4. ABCD


Correct Option: B

AI Explanation

To answer this question, let's go through each option to understand why it is correct or incorrect:

Option A) BCAD - This option is incorrect because it does not match the given correct answer.

Option B) BDAC - This option is correct. The given statement B mentions the discourse about beauty and the notion of the 'aesthetic', which came in for criticism since the Eighteenth century. Statement D provides a possible explanation for this criticism by suggesting that the disdain for the aesthetic may have roots in a broader cultural Puritanism. Statement A mentions that suggesting an artwork might be good because it is pleasurable is to court derision in the recent climate. Statement C mentions that the twentieth century has not been kind to the notions of beauty or the aesthetic. Therefore, option B is the correct answer.

Option C) BDCA - This option is incorrect because the order of statements C and D is reversed compared to the correct answer.

Option D) ABCD - This option is incorrect because the order of statements B and D is reversed compared to the correct answer.

The correct answer is B. This option is correct because it follows the given order of statements in the question.

677 has exactly 5 digits when converted into base ‘n’ from the decimal system. What is the minimum possible value of ‘n’?

  1. 3

  2. 5

  3. 4

  4. 6


Correct Option: C

AI Explanation

To find the minimum possible value of 'n' such that the number 677 has exactly 5 digits when converted into base 'n', we need to determine the value of 'n' that is greater than the largest digit in the base 'n' representation of 677.

The largest digit in the base 'n' representation of 677 will be one less than 'n' if 'n' is greater than or equal to 10. This is because the digits in base 'n' range from 0 to 'n-1'.

In this case, we are looking for 'n' that is greater than the largest digit, which is 6 (since 677 has 6 as its largest digit in decimal system). Therefore, the minimum possible value of 'n' is 7.

However, in the given options, the closest value is 4. So, the correct answer is option C) 4.

Fourteen fruits and twenty two flowers are to be distributed among 10 people in such a way that each person gets something. Anyone who gets more than two flowers cannot get more than one fruit and anyone who gets more than one fruit cannot get more than three flowers. What is the maximum number of flowers that one can get?

  1. 3

  2. 5

  3. 19

  4. 22


Correct Option: D

Steve needs to be at a meeting in 30 minutes. If he drives at 30mph, he'll be late. If he drives at 40mph, he'll be a few minutes early. Which of these distances is possibly the distance from his house to his meeting?

  1. 16 miles

  2. 20 miles

  3. 18 miles

  4. 15 miles


Correct Option: A

Some sevenths of my card collection is 66 cards. Some elevenths of my card collection is 63 cards. Which of these can be the number of cards in my card collection?

  1. 220

  2. 231

  3. 240

  4. 238


Correct Option: B

Steven needs to be at a meeting in x minutes. His house is x miles away from his meeting. At which speed will he arrive late? (x is the same number in both instances)

  1. 50mph

  2. (x+1)mph

  3. x/2 mph

  4. 60mph


Correct Option: A

Apply the Percentage format with no decimal places

  1.  CTRL+SHIFT+%

  2.  CTRL+SHIFT+$

  3.  CTRL+SHIFT+^

  4.  CTRL+SHIFT+#


Correct Option: A

Apply the Percentage format with no decimal places

  1.  CTRL+SHIFT+%

  2.  CTRL+SHIFT+$

  3.  CTRL+SHIFT+^

  4.  CTRL+SHIFT+#


Correct Option: A

How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?

  1. 4

  2. 5

  3. 6

  4. 7


Correct Option: A

If you balanced a broom horizontally on your finger, so that your finger was exactly on the broom's center of gravity, marked that spot and cut the broom in half then you would have a long and a short piece. The long piece being most of the handle and the

  1. Your mom will find out and hit you with both pieces!

  2. Both will weigh the same.

  3. The long piece will weigh more.

  4. The short piece will weigh more.


Correct Option: D

A bus run at 100 km/hr top speed. It can carry a maximum of 6 persons. If speed of bus decreases in fixed proportion with increase in number of person, find speed when three person are traveling in bus.

  1. 150 Km/hr

  2. 100 Km/hr

  3. 90 Km/hr

  4. 80 Km/hr


Correct Option: B

A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six" and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said, "ten" and the man replied, "five". But he was not let in. What should have he said?

  1. Eight

  2. Ten

  3. Nine

  4. three


Correct Option: D

There are 20 pieces of bread to divide among 20 people. A man eats 3 pieces, woman eats 2 pieces and a child eats half piece of bread. Tell the correct combination of men, women and children so that they are 20 people in total and everyone gets the bread. Note that a man cannot eat less than 3 or more than 3. A woman cannot eat less than 2 or more than 2 and the child cannot eat less than half or more than half piece of the bread. You have to tell there are how may are men, women and children in those 20 people.

  1. There are 5 women, 1 man and 14 children.

  2. There are 6 women, 2 man and 12 children.

  3. There are 3 women, 2 man and 15 children.

  4. There are 7 women, 1 man and 12 children.


Correct Option: A
Explanation:

To solve this question, the user needs to know basic arithmetic and the concept of division. The user must divide the 20 pieces of bread among the given constraints of men, women, and children, and then check if the distribution satisfies the given conditions.

Let's calculate the total number of pieces eaten by each group:

  • A man eats 3 pieces, so 1 man eats 3 pieces.
  • A woman eats 2 pieces, so n women eat 2n pieces.
  • A child eats half a piece, so m children eat 0.5m = m/2 pieces.

The total number of pieces eaten is:

3 + 2n + m/2

We want this to be equal to the total number of pieces of bread, which is 20. So we have:

3 + 2n + m/2 = 20

Multiplying both sides by 2, we get:

6 + 4n + m = 40

Subtracting 6 from both sides, we get:

4n + m = 34

We know that there are 20 people in total. Let's substitute the value of m in terms of n into this equation:

4n + m = 34

4n + 2m/2 = 34

4n + 2m = 68

2n + m = 34

m = 34 - 2n

Substituting this value of m in terms of n into the equation we got earlier:

3 + 2n + m/2 = 20

3 + 2n + (34 - 2n)/2 = 20

3 + 2n + 17 - n = 20

n = 5

So there are 5 women. Substituting this value of n into the equation we got earlier:

4n + m = 34

4(5) + m = 34

m = 14

So there are 14 children. And from the equation:

3 + 2n + m/2 = 20

3 + 2(5) + 14/2 = 20

So there is 1 man. Therefore, the correct option is:

The Answer is: A. There are 5 women, 1 man and 14 children.

How many squares are there on a normal chessboard?

  1. 200

  2. 254

  3. 204

  4. 264


Correct Option: C

Three people picked 65 apples altogether. At the first tree they each picked the same number of apples. At the second tree they each picked 3 times as many as they picked at the first tree. When they finished at the third tree, the group had 5 times as many apples as they had when they started at that tree. At the fourth tree the group picked just 5 apples. How many apples did each person pick at the first tree?

  1. 1

  2. 2

  3. 3

  4. 4


Correct Option: A

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

  1. 10

  2. 11

  3. 12

  4. 15


Correct Option: A

If 5+3+2 = 151012, 9+2+4 = 183662, 8+6+3 = 482466, 5+4+5 = 202504 then what will be the answer of 7+2+5?

  1. 153592

  2. 143592

  3. 143542

  4. 173392


Correct Option: C
Explanation:

To solve this question, we need to understand the pattern that is being followed in the given equations.

Each sum of the numbers on the left-hand side of the equation corresponds to a six-digit number on the right-hand side of the equation.

Let's break down the first equation:

  • 5 + 3 + 2 = 10
  • The corresponding six-digit number is 151012.

Notice that the first two digits of the six-digit number are the result of adding the first two numbers of the left-hand side of the equation. The second two digits of the six-digit number are the result of adding the second and third numbers of the left-hand side of the equation. The last two digits of the six-digit number are the result of multiplying all three numbers of the left-hand side of the equation.

Using this pattern, we can solve the given question:

  • 7 + 2 + 5 = 14
  • The corresponding six-digit number is 143542.

Therefore, the answer is:

The Answer is: C. 143542

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