A snack pack contains crackers, raisins, and almonds.

Question

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.

Bunuel · Accepted Answer

GMAT Club 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.

chloreton · Answer

E is the correct answer.

C:R:A is the ratio and R<90. We are asked to find A=?

Statement 1: C:A = 4:3 
We know R can be anything <90 we cant find a definitely value for A. 
Therefore, Not sufficient.

Statement 2: C:R = 5:9
We have not been given the ratio of A. Also from this 9x<90 which implies x<10. Many values are possible.
Therefore, Not sufficient.

Combining we get C:R:A =20:36:15, ie., total = 71x
Here 36x < 90 from which we get x<2.5
Now here if we put x=1, we will get a different value for A
and if we put x=2, we will get a different value for A.

Thus combining the statements also insufficient.
Therefore,  E

Adit_ · Answer

Usually in constraint problems like these, the limits declare that they are enough but not in this case:

Statement 1:
Clearly insufficient.

Statement 2:
Insufficient too.

Combining the two:

Use both given ratios and find LCM to find ratio between the 3:
Result in:
15:20:36 where crackers is 20x and raisin is 36x

Raisin is less than 90 and we see 36x will be less than 90 for 1 or 2 as the integer value for x.
Hence INSUFFICIENT.

Answer:  Option E

Adit_ · Answer

Calculations are all right but the total when combining is 71x and not 81x.

chloreton · Answer

thanks for spotting it out @ Adit_. I have edited.

Dereno · Answer

Given that Raisins are lesser than 90. We need to find the number of Almonds ?

Statement 1:

The ratio of crackers to almonds is 4:3.

Rasins is not known. Hence,  insufficient.

Statement 2:

The ratio of crackers to raisins is 5:9.

Almonds is not known. Hence,  Insufficient

Combining both statements, we get

The ratio of Almond : Cracker : Rasins = 15 : 20 : 36

36x is less than 90.

so, x can be 1 or 2. So, Raisins can be either 36 or 72.

Thus almond has two values : 15 or 30.

Hence,  Insufficient

Option E

MS26 · Answer

1. Not sufficient as we need raisin(R<90) to calculate almond (no raisin in stem)
2. C:R = 5:9, R=9K (k can be any value from 1 to 9, so R will be any value from 9 to 81) not sufficient as no specific value,
On combining both statements we get C:A:R = 20:15:36 , now here again R can have two value 36 & 72 both less than 90 so Not sufficient hence E

A snack pack contains crackers, raisins, and almonds.

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A snack pack contains crackers, raisins, and almonds.

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