One cup of nuts that contains exactly half peanuts and half cashews is

Question

One cup of nuts that contains exactly half peanuts and half cashews is added to a bowl of nuts that is exactly one third peanuts, one third cashews, and one third almonds. This results in a three-cup mixture of nuts. What fraction of the new nut mixture is peanuts?

A. 2/9
B. 5/18
C. 1/3
D. 7/18
E. 4/9

A. 2/9
B. 5/18
C. 1/3
D. 7/18
E. 4/9

yoannnesme · Accepted Answer

One cup of 1/2 p, 1/2 c is added to two cups of 1/3 p, 1/3 c, 1/3 a in order to obtain 3 cups of final mixture. Let's pick numbers for the number of nuts we have in the mixtures to find out the correct proportion.

If we have 1p and 1c in the first mixture (1 cup), then we need 4 nuts in the second mixture (2 cups). Not doable with integers, let's move on.
2p and 2 c: we need 8 nuts. Move on.
3p and 3c: we need 12 nuts. It works as it's a multiple of 3. We'd have 4p, 4c and 4a.

Now let's count the number of p and the total nuts:
p=7
total=18

Answer D: 7/18

ShankSouljaBoi · Answer

Let C be cup capacity and B be bowl capacity.

Now after addition of C to B ----> B + C = 3C ----> B=2C

Total Almonds% = (B/3 + C/2)/B+C
----> Substituting B=2C -----> 7/18

fauji · Answer

Given Info: 
 (P - peanuts, C - cashews, A - almonds, N - nuts) 
 Cup(X) : 1/2 P, 1/2 C
 Bowl : 1/3 P, 1/3 C, 1/3 A
Total quantity in Bowl: 3 (3X) cups after mixture => means bowl has original mixture equal to 2 cups (2X)before mixing.
So equation for Peanuts is

1/2 (X) + 1/3 (2X) =>7/6X

As we need to find fraction of peanuts to total mixture:
(7/6)X/3X =>  7/18

Option D

ScottTargetTestPrep · Answer

We see that the bowl originally (i.e., before the 1 cup of nuts is added) contains 2 cups of nuts, of which 2/3 cup is peanuts, 2/3 cup is cashews, and 2/3 cup is almonds.

When the 1 cup of nuts is added, 1/2 cup of peanuts and 1/2 cup of cashews are added. Therefore, now we have 2/3 + 1/2 = 4/6 + 3/6 = 7/6 cups of peanuts in the resulting 3-cup mixture of nuts. So now we have (7/6)/3 = 7/18 of the nut mixture as peanuts.

Answer: D

Hea234ven · Answer

this is an interesting question and doesn't require detailed algebraic calculation.

After mixing the first cup to the bowl, the result is that there are 3 cups, which mean 2 cups of nuts have been added extra.
we can dictate the bowl as 2 (because this would result in 2 cups, in which 2/3 is peanut,2/3 is cashew and the remaining 2/3 is almond)) and the first cup as 1 (in which 1/2 is peanuts and 1/2 is cashew).The result in the mixing would be:(1/2+1/2+2/3+2/3+2/3)=18/6. The resultant proportion of the peanuts in the new mixture would be:  +2/3(bowl amount)]/ =7/18
if u use detailed algebraic method, i think it's difficult to solve it within 2 mins.

GmatPoint · Answer

Let one cup of nuts contain 6 units of nuts.
Peanuts content in the cup = 6/2 = 3 units
Cashew content = 3 units

Since after adding a cup of nuts to the bowl, the resultant mixture was a three-cup mixture,
The volume of the bowl = 6*3 - 6 = 12 units.

Peanut content in the bowl = 12/3 = 4 units.

Total peanut content in the mixture = 4 + 3 = 7 units

Since the volume of the resultant mixture is 18 units,
Peanut content/volume of the mixture = 7/18

Thus, the correct option is D.

Ikemen · Answer

Since the final mixture is 3 cups. we have the following set up

Let 1 cup be 100, 1 bowl is then 200
1 Cup contains 50 p and 50 c
1 Bowl contains 200/3 of p/c/a
3 Cups contains 50+200/3 out of a total of 300 nuts.

so we have 50/300 + 200/900 = 350/900 = 7/18

RaahiK · Answer

Final Bowl = 3 cups = 1 original cup + 2 cups
 =   +  
 = 1/2 of peanuts in original cup + 2/3 of peanuts in 2 cups
Peanuts: 1/2 cup + 2/3 cup = 7/6 cup
The total mixture is 3 cups: (7/6)/3 = 7/18

One cup of nuts that contains exactly half peanuts and half cashews is

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One cup of nuts that contains exactly half peanuts and half cashews is

Prep Toolkit

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