Question: 16 ounces of birdseed mix contains 10% sesame seed by weight. How much sesame seed must be added to produce a mix that is 20% sesame seed by weight?
- 1 ounce
- 1.6 ounces
- 2 ounces
- 2.4 ounce
- 4 ounces
“6 ounces of birdseed mix contains 10% sesame seed by weight.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Given:
- Total 16 ounces of birdseed mix
- Contains 10% sesame seed by weight
To find:
- Amount of sesame seed must be added to produce a mix that is 20% sesame seed by weight
We are going to take the following approach to solve the problem.
In the initial mix, the amount of sesame seed is:
= 16 * 0.1
= 1.6 ounces
Let us assume that the amount of sesame seed to be mixed is “M” ounces
Therefore, after mixing,
The amount of sesame seed = 1.6 + M
The total amount of mix = 16 + M
As per the problem statement, the sesame seed accounts for 20% of the total mix amount, we can write
(16 + M) * 20% = 1.6 + M
(16 + M) * 20/100 = 1.6 + M
=> 3.2 + 0.2M = 1.6 + M
=> 0.8M = 1.6
=> M = 2
Correct Answer: C
Approach Solution 2:
Given:
- Total 16 ounces of birdseed mix
- Contains 10% sesame seed by weight
To find:
- Amount of sesame seed must be added to produce a mix that is 20% sesame seed by weight
We are going to take the following approach to solve the problem.
In 16 Ounces, we have 10% sesame seed i.e. 1.6 ounce.
Now, let us assume x ounce of sesame seed needed to make mixture that contains 20% of sesame seed
Hence, the equation stands:
=> (1.6+x)/(16+x)= 1/5
=> by cross-multiplication, 8+5x= 16+x
=> 4x=8
=> x=2
Correct Answer: C
Approach Solution 3:
Given:
16 ounces of mixed birdseed.
Contains 10% sesame seed in its composition.
To determine
To make a mixture that contains 20% sesame seed by weight, the right amount of sesame seed must be added.
The following approach will be used to solve the problem.
10% or 1.6 ounces of sesame seeds are present in 16 ounces.
Let's now assume that x ounces of sesame seeds are required to generate a combination with 20% sesame seeds.
As a result, the following equation is true:
=> (1.6+x)/(16+x)=1/5
=> via cross-multiplication, 8+5x= 16+x
=> 4x=8
=> x=2
Correct Answer: C
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