XAT 2023 — QA & DI Question 28
Go through the information given below, and answer the THREE questions that follow.
The table captures Age and Gender distribution of Covid Positive Cases in a country. However, a part of data is missing, represented through unknown categories.
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The addition of 7 distinct positive integers is 1740. What is the largest possible “greatest common
divisor” of these 7 distinct positive integers?
Answer & solution
- A
42
60
- C
74
- D
140
- E
None of these
Let the greatest common divisor be m.
Now, the 7 numbers will be m × a, m × b, m × c, ..., m × g.
⇒ m × a + m × b + m × c + ... + m × g = 1740
⇒ m(a + b + c + ... + g) = 1740 ...(1)
For m to be highest possible, (a + b + c + ... + g) should be least possible.
Least possible value of (a + b + c + ... + g) = (1 + 2 + 3 + ... + 7) = 28
∴ (a + b + c + ... + g) ≥ 8
Now, (1) can be written as
m(a + b + c + ... + g) = 1740 = 22 × 3 × 5 × 29
⇒ least possible value based on the given condition = 29
∴ m = 22 × 3 × 5 = 60
Hence, option (b).