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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
Five archeologists – P, Q, R, S and T were looking to gather artifacts of a surveyed site. Each one of them was assigned to a different site that is numbered as: A413, B201, C302, D109 and F507. Each archeologist found a different number of coins at his/her respective site. All coins excavated by each archeologist are of the same denomination. The coins from different sites had different denominations, which is one among 1, 2, 3, 4 and 5.
The highest number of coins were excavated at site B201.
P, whose excavation resulted in the least number of coins, had the highest value in denomination.
The total number of coins excavated at the five sites together is 75, and the total value (i.e. value = # of coins x denomination) of coins at all sites together is 183.
The number of coins excavated by each archeologist is an odd multiple of 3.
Q who was assigned site D109, excavated coins that had the highest value.
The number of coins discovered at site A413 is 15 this site was assigned to R. S was assigned site C302.
The denomination of coins excavated by R is greater then those excavated by S.
Question 1
How many coins were excavated at site A413?
Question 2
What is the highest value of coins excavated from among the five sites?
Question 3
What is the denomination of coins excavated at site C302?
Question 4
What is the number of coins excavated whose denomination is 4?
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𝘐𝘯 𝘮𝘢𝘬𝘪𝘯𝘨 𝘢𝘯 𝘪𝘯𝘷𝘦𝘴𝘵𝘮𝘦𝘯𝘵 𝘥𝘦𝘤𝘪𝘴𝘪𝘰𝘯, 𝘪𝘯𝘷𝘦𝘴𝘵𝘰𝘳𝘴 𝘮𝘶𝘴𝘵 𝘳𝘦𝘭𝘺 𝘰𝘯 𝘵𝘩𝘦𝘪𝘳 𝘰𝘸𝘯 𝘦𝘹𝘢𝘮𝘪𝘯𝘢𝘵𝘪𝘰𝘯 𝘰𝘧 𝘵𝘩𝘦 𝘪𝘴𝘴𝘶𝘦𝘳 𝘢𝘯𝘥 𝘵𝘩𝘦 𝘵𝘦𝘳𝘮𝘴 𝘰𝘧 𝘵𝘩𝘦 𝘰𝘧𝘧𝘦𝘳𝘪𝘯𝘨, 𝘪𝘯𝘤𝘭𝘶𝘥𝘪𝘯𝘨 𝘵𝘩𝘦 𝘮𝘦𝘳𝘪𝘵𝘴 𝘢𝘯𝘥 𝘳𝘪𝘴𝘬𝘴 𝘪𝘯𝘷𝘰𝘭𝘷𝘦𝘥. 𝘋𝘐𝘛 𝘈𝘨𝘛𝘦𝘤𝘩 𝘩𝘢𝘴 𝘧𝘪𝘭𝘦𝘥 𝘢 𝘍𝘰𝘳𝘮 𝘊 𝘸𝘪𝘵𝘩 𝘵𝘩𝘦 𝘚𝘦𝘤𝘶𝘳𝘪𝘵𝘪𝘦𝘴 𝘢𝘯𝘥 𝘌𝘹𝘤𝘩𝘢𝘯𝘨𝘦 𝘊𝘰𝘮𝘮𝘪𝘴𝘴𝘪𝘰𝘯 𝘪𝘯 𝘤𝘰𝘯𝘯𝘦𝘤𝘵𝘪𝘰𝘯 𝘸𝘪𝘵𝘩 𝘪𝘵𝘴 𝘰𝘧𝘧𝘦𝘳𝘪𝘯𝘨, 𝘢 𝘤𝘰𝘱𝘺 𝘰𝘧 𝘸𝘩𝘪𝘤𝘩 𝘮𝘢𝘺 𝘣𝘦 𝘰𝘣𝘵𝘢𝘪𝘯𝘦𝘥 𝘩𝘦𝘳𝘦: https://bit.ly/4bzuWCi
✅ Answers & Explanations
From the clues:
Five archaeologists: P, Q, R, S, T
Five sites: A413, B201, C302, D109, F507
Denominations: 1, 2, 3, 4, 5
Total number of coins = 75
Total value of coins = 183
Each number of coins is a distinct odd multiple of 3.
Step 1: Determine the number of coins
The five distinct odd multiples of 3 that add up to 75 are:
3, 9, 15, 21, 27
because:
3 + 9 + 15 + 21 + 27 = 75
We know from clue 6:
R → A413 → 15 coins
From clue 2, P excavated the least number of coins.
Therefore:
P → 3 coins
From clue 1, the highest number of coins was excavated at B201.
Therefore:
B201 → 27 coins
Since Q is at D109, R is at A413, and S is at C302, only P and T can be assigned to B201 and F507.
But P has only 3 coins, whereas B201 has 27.
Therefore:
T → B201 → 27 coins
P → F507 → 3 coins
We now have:
Archaeologist | Site | Coins |
|---|---|---|
P | F507 | 3 |
Q | D109 | 9 or 21 |
R | A413 | 15 |
S | C302 | 9 or 21 |
T | B201 | 27 |
Step 2: Determine denominations
P has the highest denomination.
Since the denominations are 1, 2, 3, 4 and 5:
P → denomination 5
Hence P's coin value is:
3 × 5 = 15
The remaining denominations 1, 2, 3, 4 must be assigned to Q, R, S and T.
We also know:
Denomination of R > denomination of S
And Q has the highest total value.
The total value across all five archaeologists is 183.
Therefore, the remaining four must contribute:
183 − 15 = 168
Step 3: Determine Q and S's coin counts
Suppose:
Q = 9 coins and S = 21 coins
Since Q must have the highest value, this becomes extremely restrictive because Q has only 9 coins while T has 27 and R has 15.
Checking the possible denomination assignments does not satisfy all the given conditions along with the total of 183.
Therefore:
Q = 21 coins
S = 9 coins
So we have:
Archaeologist | Site | Coins |
|---|---|---|
P | F507 | 3 |
Q | D109 | 21 |
R | A413 | 15 |
S | C302 | 9 |
T | B201 | 27 |
Step 4: Find the remaining denominations
We need to assign denominations 1, 2, 3, 4 to Q, R, S and T such that:
21(Q denomination) + 15(R denomination) + 9(S denomination) + 27(T denomination) = 168
Also:
R denomination > S denomination
The assignment satisfying these conditions is:
Q = 3
R = 4
S = 2
T = 1
Check the total value:
P: 3 × 5 = 15
Q: 21 × 3 = 63
R: 15 × 4 = 60
S: 9 × 2 = 18
T: 27 × 1 = 27
Therefore:
15 + 63 + 60 + 18 + 27 = 183 ✓
Also, Q has the highest value:
Q = 63, which is greater than R's 60, T's 27, S's 18 and P's 15.
Final Table
Archaeologist | Site | Coins | Denomination | Value |
|---|---|---|---|---|
P | F507 | 3 | 5 | 15 |
Q | D109 | 21 | 3 | 63 |
R | A413 | 15 | 4 | 60 |
S | C302 | 9 | 2 | 18 |
T | B201 | 27 | 1 | 27 |
Answers to the Questions
1. How many coins were excavated at site A413?
A413 was assigned to R, and clue 6 directly states that 15 coins were found there.
Answer: 15
2. What is the highest value of coins excavated from among the five sites?
Q excavated 21 coins of denomination 3:
21 × 3 = 63
Answer: 63
3. What is the denomination of coins excavated at site C302?
C302 was assigned to S, whose denomination is 2.
Answer: 2
4. What is the number of coins excavated whose denomination is 4?
R had denomination 4 and excavated 15 coins.
Answer: 15
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