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14 Dec 2022, 02:13
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C
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Difficulty:
45%
(medium)
Question Stats:
66% (01:26) correct
34%
(01:13)
wrong
based on 103
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A list contains 7 positive integers. What is the value of the smallest integer in the set?
(1) The highest term in the set is 37
(2) When arranged in increasing order, the difference between any two consecutive terms is at least 6
(1) The highest term in the set is 37
(2) When arranged in increasing order, the difference between any two consecutive terms is at least 6
14 Dec 2022, 03:48
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bambinobirbante
A list contains 7 positive integers. What is the value of the smallest integer in the set?
(1) The highest term in the set is 37
(2) When arranged in increasing order, the difference between any two consecutive terms is at least 6
(1) The highest term in the set is 37
(2) When arranged in increasing order, the difference between any two consecutive terms is at least 6
Given
- The list has 7 integers
- All the integers are positive
Question - What is the value of the smallest integer in the set?
Statement 1
The highest term in the set is 37
Merely knowing the highest terms doesn't help. The smallest integer can be any value between 1 and 37, both inclusive.
The statement is insufficient and we can eliminate A and D
Statement 2
When arranged in increasing order, the difference between any two consecutive terms is at least 6
Just like Statement1, Statement 2 doesn't provide much information. We can have infinite possibilities of the lowest term.
Eliminate B
Combined
The statements combined tells us that maximum value is 37 and the difference between two any two consecutive terms is at least 6.
Hence, if we consider the difference to be exactly 6, the lowest term is 1. If we increase the difference between any two consecutive terms, the lowest term will not be positive.
Hence we have an unique answer.
Option C
14 Dec 2022, 07:37
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bambinobirbante
A list contains 7 positive integers. What is the value of the smallest integer in the set?
(1) The highest term in the set is 37
(2) When arranged in increasing order, the difference between any two consecutive terms is at least 6
(1) The highest term in the set is 37
(2) When arranged in increasing order, the difference between any two consecutive terms is at least 6
Solution:
Pre Analysis:
- A list contains 7 positive integers
- We are asked the smallest integer in the set
Statement 1: The highest term in the set is 37
- This will not help us get the smallest term in the set
- Thus, statement 1 alone is not sufficient and we can eliminate options B, C and E
Statement 2: When arranged in increasing order, the difference between any two consecutive terms is at least 6
- We are given difference between any two consecutive terms = 6
- From this we cannot say what the smallest term in the set is
- Thus, statement 2 alone is also not sufficient
Combining:
- Smallest positive integer is 1. So, let us assume the smallest term in the list is 1
- If the first term (smallest) is 1 and the seventh term (highest) is 37, then the difference between any two has to be 6 and not more than that
- Thus, upon combining it is sufficient to say that the smallest term in the list is 1
Hence the right answer is Option C
