The question is from Permutation and Combination. A question on possible values. We need to find the number of possible positive integers that satisfies the equation. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 17: 2a + 5b = 103. How many pairs of positive integer values can a, b take such that a > b?

- 7
- 9
- 14
- 15

for free

Starts Sat, July 20th, 2019

Let us find the one pair of values for a, b.

a = 4, b = 19 satisfies this equation.

2*4 + 5*19 = 103.

Now, if we increase ‘a’ by 5 and decrease ‘b’ by 2 we should get the next set of numbers. We can keep repeating this to get all values.

Let us think about why we increase ‘a’ by 5 and decrease b by 2.

a = 4, b = 19 works.

Let us say, we increase ‘a’ by n, then the increase would be 2n.

This has to be offset by a corresponding decrease in b.

Let us say we decrease b by ‘m’.

This would result in a net drop of 5m.

In order for the total to be same, 2n should be equal to 5m.

The smallest value of m, n for this to work would be 2, 5.

a = 4, b = 19

a = 9, b = 17

a = 14, b = 15

..

And so on till

a = 49, b = 1

We are also told that ‘a’ should be greater than ‘b’, then we have all combinations from (19, 13) … (49, 1).

7 pairs totally.

The question is **"2a + 5b = 103. How many pairs of positive integer values can a, b take such that a > b?"**

Choice A is the correct answer.

Enroll at 32000/-

Next Weekend Batch Starts Sat, July 13th, 2019

Register Online, get Rs 4000 off

Personalised attention, Small batch sizes.

1. Digit Numbers | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

6. Rearranging Letters | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

Copyrights © 2019 All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

10-C, Kalinga Colony, Bobbili Raja Salai

K.K.Nagar, Chennai. India. Pin - 600 078

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com