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A snack pack contains crackers, raisins, and almonds. If there are fewer than 90 raisins in the pack, how many almonds are in the pack?
(1) The ratio of crackers to almonds is 4:3.
(2) The ratio of crackers to raisins is 5:9.
(1) The ratio of crackers to almonds is 4:3.
(2) The ratio of crackers to raisins is 5:9.
26 Apr 2026, 13:50
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Official Solution:
A snack pack contains crackers, raisins, and almonds. If there are fewer than 90 raisins in the pack, how many almonds are in the pack?
Let \(C\) = crackers, \(R\) = raisins, \(A\) = almonds.
We are told \(R < 90\) and asked for \(A\).
(1) The ratio of crackers to almonds is \(4:3\).
The number of almonds, \(A\), can be any positive multiple of 3. Not sufficient.
(2) The ratio of crackers to raisins is \(5:9\).
The number of almonds, \(A\), is not linked at all. Not sufficient.
(1)+(2) Given:
\(C:A = 4:3\) and \(C:R = 5:9\)
Adjust the ratios so that the number corresponding to \(C\) matches by multiplying the first ratio by 5 and the second by 4:
\(C:A = 20:15\) and \(C:R = 20:36\)
So:
\(C:A:R = 20:15:36\)
Since \(R < 90\), the number of raisins, \(R\), can be 36 or 72. Respectively, the number of almonds, \(A\), can be 15 or 30. Not sufficient.
Answer: E
A snack pack contains crackers, raisins, and almonds. If there are fewer than 90 raisins in the pack, how many almonds are in the pack?
Let \(C\) = crackers, \(R\) = raisins, \(A\) = almonds.
We are told \(R < 90\) and asked for \(A\).
(1) The ratio of crackers to almonds is \(4:3\).
The number of almonds, \(A\), can be any positive multiple of 3. Not sufficient.
(2) The ratio of crackers to raisins is \(5:9\).
The number of almonds, \(A\), is not linked at all. Not sufficient.
(1)+(2) Given:
\(C:A = 4:3\) and \(C:R = 5:9\)
Adjust the ratios so that the number corresponding to \(C\) matches by multiplying the first ratio by 5 and the second by 4:
\(C:A = 20:15\) and \(C:R = 20:36\)
So:
\(C:A:R = 20:15:36\)
Since \(R < 90\), the number of raisins, \(R\), can be 36 or 72. Respectively, the number of almonds, \(A\), can be 15 or 30. Not sufficient.
Answer: E
