### Quantitative Section : GMAT Sample Problem Solving Ability

**Permutation and Combination**

1. There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

1. 2 * 19!

2. 18! * 18

3. 19! * 18

4. 2 * 18!

Ans : D

2. How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?

1. 5!

2. 4!

3. 6! – 2!

4. 6! / 2!

Ans : B

3. There are 12 yes or no questions. How many ways can these be answered?

1. 1024

2. 2048

3. 4096

4. 144

Ans : C

4. How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?

1. 256

2. 12

3. 81

4. None of these

Ans : C

5. A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

1. 9

2. 26

3. 126

4. 3920

Ans : C

6. How many numbers are there between 100 and 1000 such that atleast one of their digits is 6?

1. 648

2. 258

3. 654

4. 252

Ans : D

7. How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?

1. 5 10

2. 10 5

3. 10P5

4. 10C5

Ans : A

8. In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?

1. 9!/4

2. 9!/(4!*5!)

3. 4!*5!

4. None of these

Ans : C

9. In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

1. 15!/(8!)

2. 7!*8!

3. (15C8)*6!*7!

4. 2*(15C7)*6!*7!

Ans : C

10. If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

1. 24

2. 31

3. 32

4. 30

Ans : C

1. How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?

1. 16C7 * 7!

2. 12C4 * 4C3 * 7!

3. 12C3 * 4C4

4. 12C4 * 4C3

Ans : B

2. In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

1. 5C3

2. 5P3

3. 53

4. 35

Ans : D

3. How many number of times will the digit ‘7’ be written when listing the integers from 1 to 1000?

1. 271

2. 300

3. 252

4. 304

Ans : B

4. There are 6 boxes numbered 1, 2,…6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is

1. 5

2. 21

3. 33

4. 60

Ans : B

5. What is the value of 1*1! + 2*2! + 3!*3! + ………… n*n!, where n! means n factorial or n(n-A(n-2)…1

1. n(n-A(n-A!))

2. (n+A!)/(n(n-A))

3. (n+A! – n!)

4. (n + A! – 1!)

Ans : D

6. There are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?

1. 15624

2. 16384

3. 6144

4. 240

Ans : A

7. In how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?

1. 10! – 2!

2. 9! – 2!

3. 10! – 9!

4. None of these

Ans : D

8. How many five digit numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 which are divisible by 3, without repeating the digits?

1. 15

2. 96

3. 216

4. 120

Ans : C

9. How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively?

1. 8! / 2!

2. 8! – 2!

3. 6!

4. 8! – 2*7!

Ans : C

10. Four dice are rolled simultaneously. What is the number of possible outcomes in which at least one of the die shows 6?

1. 6! / 4!

2. 625

3. 671

4. 1296

Ans : C

**Percentage**

1. A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?

1. 33.33%

2. 75%

3. 300%

4. 150%

Ans : C

2. A merchant buys two articles for Rs.600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?

1. Rs. 404.80

2. Rs. 440

3. Rs. 536.80

4. Rs. 160

Ans : A

3. A trader professes to sell his goods at a loss of 8% but weights 900 grams in place of a kg weight. Find his real loss or gain per cent.

1. 2% loss

2. 2.22% gain

3. 2% gain

4. None of these

Ans : B

4. Rajiv sold an article for Rs.56 which cost him Rs.x. If he had gained x% on his outlay, what was his cost?

1. Rs. 40

2. Rs. 45

3. Rs. 36

4. Rs. 28

Ans : A

5. A trader buys goods at a 19% Aount on the label price. If he wants to make a profit of 20% after allowing a Aount of 10%, by what % should his marked price be greater than the original label price?

1. +8%

2. -3.8%

3. +33.33%

4. None of these

Ans : A

6. If apples are bought at the rate of 30 for a rupee. How many apples must be sold for a rupee so as to gain 20%?

1. 28

2. 25

3. 20

4. 22

Ans : B

7. One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and recieves Rs. 120 and a shirt. Then find the price of the shirt.

1. Rs. 80

2. Rs. 100

3. Rs. 120

4. Cannot be determined

Ans : C

8. Two merchants sell, each an article for Rs.1000. If Merchant A computes his profit on cost price, while Merchant B computes his profit on selling price, they end up making profits of 25% respectively. By how much is the profit made by Merchant B greater than that of Merchant A?

1. Rs.66.67

2. Rs. 50

3. Rs.125

4. Rs.200

Ans : B

9. A merchant marks his goods in such a way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin?

1. 25%

2. 50%

3. 100%

4. 66.67%

Ans : C

10. A merchant marks his goods up by 75% above his cost price. What is the maximum % Aount that he can offer so that he ends up selling at no profit or loss?

1. 75%

2. 46.67%

3. 300%

4. 42.85%

Ans : D

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