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27 Jan 2025, 01:30
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C
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Difficulty:
35%
(medium)
Question Stats:
70% (01:41) correct
30%
(01:34)
wrong
based on 121
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A particular party mix contains pretzels, chips, and nuts. If there are fewer than 60 chips in the mix, how many nuts are in the party mix?
(1) The ratio of pretzels to nuts is 5:2
(2) The ratio of pretzels to chips is 3:7
(1) The ratio of pretzels to nuts is 5:2
(2) The ratio of pretzels to chips is 3:7
27 Jan 2025, 08:25
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Given Chips (c) < 60
Then Nuts (n) = ?
(1) The ratio of pretzels to nuts is 5:2
This gives us ratio p:n = 5:2
This only gives us that nuts are a multiple of 2. But there can be many such answers below 60.
Hence, does not help us much
(2) The ratio of pretzels to chips is 3:7
This gives us ration p:c = 3:7
This tells us nothing about nuts.
Hence, does not help us much
Taking 1 and 2 together,
n:p
p:c
2:5 (i)
3:7 (ii)
Hence, combining to form the ratio of 3: (Multiplying (i) by 3 and (ii) by 5, i.e basically taking LCM of two multiples of p known)
n:p:c = 6:15:35
Now we know that Chips are a multiple of 35.
As the number of chips can't be a fraction,
We get the only multiple of 35 possible is 35*1=35 (As 35*2=70>60)
Hence, al the ratios have 1 as multiplier constant.
Hence no. of Nuts= 6
IMO Ans C
Then Nuts (n) = ?
(1) The ratio of pretzels to nuts is 5:2
This gives us ratio p:n = 5:2
This only gives us that nuts are a multiple of 2. But there can be many such answers below 60.
Hence, does not help us much
(2) The ratio of pretzels to chips is 3:7
This gives us ration p:c = 3:7
This tells us nothing about nuts.
Hence, does not help us much
Taking 1 and 2 together,
n:p
p:c
2:5 (i)
3:7 (ii)
Hence, combining to form the ratio of 3: (Multiplying (i) by 3 and (ii) by 5, i.e basically taking LCM of two multiples of p known)
n:p:c = 6:15:35
Now we know that Chips are a multiple of 35.
As the number of chips can't be a fraction,
We get the only multiple of 35 possible is 35*1=35 (As 35*2=70>60)
Hence, al the ratios have 1 as multiplier constant.
Hence no. of Nuts= 6
IMO Ans C
27 Jan 2025, 09:22
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Question Breakdown:
- The party mix contains pretzels, chips, and nuts.
- There are fewer than 60 chips in the mix.
- We need to determine how many nuts are in the party mix.
Let:
- P = number of pretzels
- C = number of chips
- N = number of nuts
We are given that C < 60 and asked to find N.
Statement 1: The ratio of pretzels to nuts is 5:2.
- This means P/N = 5/2, so P = (5/2) * N.
- This alone doesn’t provide enough information to calculate N because we don’t know the number of pretzels or chips. We need more data to find N.
- Statement 1 is insufficient.
Statement 2: The ratio of pretzels to chips is 3:7.
- This means P/C = 3/7, so P = (3/7) * C.
- We know C < 60, but we don't know the exact values for C or N. Therefore, this statement alone doesn't help us calculate the number of nuts.
- Statement 2 is insufficient.
Combining both statements:
- From Statement 1: P = (5/2) * N.
- From Statement 2: P = (3/7) * C.
- Equating the two expressions for P:
(5/2) * N = (3/7) * C.
- Solving for C in terms of N:
C = (7/3) * (5/2) * N = (35/6) * N.
- Since C < 60, we find a range for N:
(35/6) * N < 60.
- Simplifying: N < (60 * 6) / 35 = 360 / 35 ≈ 10.29.
- Therefore, N must be less than 10. Since N is a whole number, N = 10.
- Therefore, N = 10.
Conclusion:
Both statements together are sufficient to determine the number of nuts in the party mix.
Answer: C. Both statements together are sufficient.
- The party mix contains pretzels, chips, and nuts.
- There are fewer than 60 chips in the mix.
- We need to determine how many nuts are in the party mix.
Let:
- P = number of pretzels
- C = number of chips
- N = number of nuts
We are given that C < 60 and asked to find N.
Statement 1: The ratio of pretzels to nuts is 5:2.
- This means P/N = 5/2, so P = (5/2) * N.
- This alone doesn’t provide enough information to calculate N because we don’t know the number of pretzels or chips. We need more data to find N.
- Statement 1 is insufficient.
Statement 2: The ratio of pretzels to chips is 3:7.
- This means P/C = 3/7, so P = (3/7) * C.
- We know C < 60, but we don't know the exact values for C or N. Therefore, this statement alone doesn't help us calculate the number of nuts.
- Statement 2 is insufficient.
Combining both statements:
- From Statement 1: P = (5/2) * N.
- From Statement 2: P = (3/7) * C.
- Equating the two expressions for P:
(5/2) * N = (3/7) * C.
- Solving for C in terms of N:
C = (7/3) * (5/2) * N = (35/6) * N.
- Since C < 60, we find a range for N:
(35/6) * N < 60.
- Simplifying: N < (60 * 6) / 35 = 360 / 35 ≈ 10.29.
- Therefore, N must be less than 10. Since N is a whole number, N = 10.
- Therefore, N = 10.
Conclusion:
Both statements together are sufficient to determine the number of nuts in the party mix.
Answer: C. Both statements together are sufficient.
