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SET 1 — 🔍 CAT Level
Each of A, B, C, D and E has a certain number of candies. They together have 400 candies. None of them has less than 40 candies. No two among them have the same number of candies.
Also,
i. A has the same number of candies as B and C put together.
ii. C has 8 more candies than the square of an integer.
iii. The number of candies with A is the square of an integer, and is more than the number of candies with D.
iv. The number of candies with B is the square of an integer.
v. The number of candies with D and E are in the ratio 4 : 3.
Question 1
How many candies does E have?
Question 2
How many candies do B and D together have?
Question 3
What is the difference in the number of candies with C and E?
Question 4
The maximum difference in the number of candies between any two persons is
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✅ Answers & Explanations
Set 1
Let the candies with A, B, C, D and E be A, B, C, D and E.
Given:
A = B + C
Total = 400
So,
A + B + C + D + E = 400
Since A = B + C,
A + A + D + E = 400
2A + D + E = 400
Also, D : E = 4 : 3
So, let D = 4x and E = 3x.
Then,
2A + 4x + 3x = 400
2A + 7x = 400
Now A is a square number and A > D.
Possible square numbers for A above 40 and below 200:
49, 64, 81, 100, 121, 144, 169, 196
Check 2A + 7x = 400.
So,
7x = 400 - 2A
Only A = 144 gives a valid integer value for x.
7x = 400 - 288 = 112
x = 16
So,
D = 4x = 64
E = 3x = 48
Now,
A = 144
A = B + C
B is a square number and C is 8 more than a square number.
B + C = 144
Possible B values:
49, 64, 81, 100
If B = 100,
C = 44
C = 36 + 8, which satisfies the condition.
So,
A = 144
B = 100
C = 44
D = 64
E = 48
All are different and all are at least 40.
Answers:
E has 48 candies.
B and D together have 100 + 64 = 164 candies.
Difference between C and E = 48 - 44 = 4 candies.
Maximum difference = 144 - 44 = 100 candies.
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!