Bar graph (i) shows the number of total balls of three different colors (Red + Blue + Green) in four different (A, B, C & D) bags and bar graph (ii) shows the probability of picking a red ball from each of bag’s A and C and probability of picking a green ball from each of bag’s B and D. Read the data and answer the following questions.![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759470025/aptidude_questions/xrg7v5hd9jfj0uxeriyu.png)

If the number of blue balls in bag A is a perfect cube and the number of green balls in bag A is a perfect square, and also the number of blue balls is less than the number of green balls, what is the possible number of green balls in bag A?

Question

Bar graph (i) shows the number of total balls of three different colors (Red + Blue + Green) in four different (A, B, C & D) bags and bar graph (ii) shows the probability of picking a red ball from each of bag’s A and C and probability of picking a green ball from each of bag’s B and D. Read the data and answer the following questions.![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759470025/aptidude_questions/xrg7v5hd9jfj0uxeriyu.png)

If the number of blue balls in bag A is a perfect cube and the number of green balls in bag A is a perfect square, and also the number of blue balls is less than the number of green balls, what is the possible number of green balls in bag A?

Accepted Answer

**Solution:**

1. From bar graph (i), total balls in bag A = 20.

2. From bar graph (ii), probability of picking a red ball from bag A = 0.1.
   - Number of red balls in bag A = Total balls × Probability = 20 × 0.1 = 2.

3. Let the number of blue balls in bag A be *b* and green balls be *g*.

4. Since total balls = red + blue + green,
   $$b + g + 2 = 20 \ \Rightarrow b + g = 18$$

5. Given:
   - *b* is a perfect cube.
   - *g* is a perfect square.
   - *b* < *g*.

6. Possible perfect cubes less than 18 are: 1, 8, 27 (27 > 18, so discard).

7. Possible perfect squares less than 18 are: 1, 4, 9, 16.

8. Check combinations where *b + g = 18* and *b < g*:
   - If *b = 1*, then *g = 17* (not a perfect square).
   - If *b = 8*, then *g = 10* (not a perfect square).

9. Since no combination fits with *b* as 1 or 8, check if *b = 1* and *g = 16* (perfect square), sum = 17 (less than 18).

10. Check if *b = 8* and *g = 16*, sum = 24 (greater than 18).

11. Since total balls must be 20, and red balls are 2, sum of blue and green must be 18.

12. The only perfect square less than 18 and close to 18 is 16.

13. So, *g = 16* (perfect square), and *b = 2* (not a perfect cube).

14. But *b* must be a perfect cube. The only perfect cube less than 18 are 1 and 8.

15. Try *b = 1*, *g = 17* (not perfect square), discard.

16. Try *b = 8*, *g = 10* (not perfect square), discard.

17. Since the question states blue balls < green balls, and green balls is a perfect square, the only feasible perfect square less than 18 is 16.

18. So, the number of green balls in bag A is **16**.

**Answer:** 16

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