Latika, Garima and Sanchi draw 3 cards each from 9 cards numbered from 1 to 9.
Latika: L, Garima: G, Sanchi: S
L : The product of my numbers is 48.
G : The sum of my numbers is 15.
S : The product of my numbers is 63.
What is the sum of numbers on the cards drawn of Latika and Sanchi?

Options

A. 28
B. 32
C. 30
D. 45

Answer

To solve the problem, we need to find the numbers drawn by Latika (L) and Sanchi (S) based on the given conditions. Let's break it down step by step.

### Step 1: Identify Latika's Numbers
Latika states that the product of her numbers is 48. We need to find three numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} whose product equals 48.

**Possible combinations:**
- \( 1 \times 6 \times 8 = 48 \)
- \( 2 \times 4 \times 6 = 48 \)

Thus, Latika's possible sets of numbers are:
1. {1, 6, 8}
2. {2, 4, 6}

### Step 2: Identify Garima's Numbers
Garima states that the sum of her numbers is 15. We also know that she has drawn three cards from the remaining numbers after Latika's selection.

**Remaining numbers after Latika's selection:**
- If Latika has {1, 6, 8}, remaining numbers are {2, 3, 4, 5, 7, 9}.
- If Latika has {2, 4, 6}, remaining numbers are {1, 3, 5, 7, 8, 9}.

We need to find three numbers from these remaining sets that sum to 15.

1. **For Latika's set {1, 6, 8}:**
- Possible combinations from {2, 3, 4, 5, 7, 9} that sum to 15:
- {2, 5, 8}
- {3, 4, 8}
- {7, 8} (not valid as it doesn't have 3 numbers)

2. **For Latika's set {2, 4, 6}:**
- Possible combinations from {1, 3, 5, 7, 8, 9} that sum to 15:
- {1, 5, 9}
- {3, 5, 7}

### Step 3: Identify Sanchi's Numbers
Sanchi states that the product of her numbers is 63. We need to find three numbers from the remaining set that multiply to 63.

**Possible combinations for Sanchi:**
- \( 1 \times 7 \times 9 = 63 \)
- \( 3 \times 3 \times 7 = 63 \) (not valid as we can't have duplicate cards)

### Step 4: Determine Valid Combinations
Now we check the validity of the combinations for Latika and Garima's numbers based on the remaining cards.

1. **If Latika has {1, 6, 8}:**
- Garima could have {2, 5, 8} (not valid as 8 is already taken).
- Garima could have {3, 4, 8} (not valid as 8 is already taken).

2. **If Latika has {2, 4, 6}:**
- Garima could have {1, 5, 9} (valid).
- Garima could have {3, 5, 7} (valid).

### Step 5: Find Sanchi's Numbers
If Garima has {1, 5, 9}, then Sanchi can only have {3, 7} which does not work since she needs three cards.

If Garima has {3, 5, 7}, then the remaining numbers for Sanchi could be {1, 2, 9} which gives:
- \( 1 \times 7 \times 9 = 63 \) (valid).

### Step 6: Calculate the Sum
Now we have:
- Latika's numbers: {2, 4, 6}
- Sanchi's numbers: {1, 7, 9}

Now we calculate the sum of the numbers on the cards drawn by Latika and Sanchi:
- Sum = \( 2 + 4 + 6 + 1 + 7 + 9 \)

Calculating:
- Latika's sum: \( 2 + 4 + 6 = 12 \)
- Sanchi's sum: \( 1 + 7 + 9 = 17 \)

Total sum = \( 12 + 17 = 29 \)

### Final Answer
The sum of the numbers on the cards drawn by Latika and Sanchi is **29**.