OG 2020: Question No. 313
Jack picked 76 apples. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many apples did he keep? (t and y are positive integers.)
- y ≥ 15 and t = 2
- y = 17
| Source | OG 2020 |
| Type | Data Sufficiency |
| Topi | Algebra |
| Sub-Topic | Linear Equations/ Inequalities |
| Difficulty | Easy – Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- Jack picked 76 apples.
- Of these 76 apples, he sold 4y apples to Juanita and 3t apples to Sylvia (y and t are positive integers).
- After selling them, Jack kept the remaining apples.
We need to determine
- The number of apples that Jack kept with himself.
As Jack sold 4y and 3t apples from a total of 76 apples, he is left with 76 – (4y + 3t) apples.
- Hence, to determine the number of apples left, we need to know the values of both y and t or 4y +3t.
With this understanding, let us now analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, y ≥ 15 and t = 2.
- From this statement, we know the exact value of t.
- However, from the given range of y ≥ 15, we cannot determine the exact value of y.
- For example, if y = 15, number of apples left = 76 – 4 × 15 – 3 × 2 = 10
- Alternatively, if y = 16, number of apples left = 76 – 4 × 16 – 3 × 2 = 6
As we don’t know the exact value of y, statement 1 is not sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, y = 17.
- However, from this statement, we cannot determine the exact value of t.
Hence, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Combining the information from both statements, we can say
- y = 17 and t = 2
As we know the values of both y and t, we can determine the number of apples left with Jack.
Hence, the correct answer choice is option C.
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