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Bunuel
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Two sets of 4 consecutive positive integers have exactly one integer 03 Nov 2022, 07:03
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D
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Difficulty:

25% (medium)

Question Stats:

77% (01:22) correct 23% (01:13) wrong based on 137 sessions

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Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.
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D
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sadshen
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Two sets of 4 consecutive positive integers have exactly one integer 04 Nov 2022, 04:51
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Difference Set 1 -Set 2= 3+3+3+3=12 (D)
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rajtare
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Two sets of 4 consecutive positive integers have exactly one integer 05 Nov 2022, 07:47
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Bunuel
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.
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let number in set a = x-2, x-1, x, x+1
let number in set b = x+1, x+2,x+3,x+4

sum of set a = 4x-2
sum of set b = 4x+10
diff of b-a = 4x+10-4x+2 = 12

hence correct answer should be option D
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Two sets of 4 consecutive positive integers have exactly one integer 17 Aug 2025, 18:35
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Hello, i didn't understand the language the 'The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?'

This means the largest number in the set? Please help.
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Two sets of 4 consecutive positive integers have exactly one integer 18 Aug 2025, 00:25
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MegB07
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

Hello, i didn't understand the language the 'The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?'

This means the largest number in the set? Please help.
Show more

We are told that two sets of four consecutive integers have exactly one integer in common. Because the sets are consecutive and share only one integer, it must be that the largest number of the smaller set equals the smallest number of the larger set.

The question then asks: how much greater is the sum of the set with larger numbers than the sum of the smaller set.

Example:

  • Smaller set: 1, 2, 3, 4
  • Larger set: 4, 5, 6, 7

The “set with greater numbers” is 4, 5, 6, 7.

So the problem is simply comparing the sum of the larger set with the sum of the smaller set, not the largest individual element.
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Two sets of 4 consecutive positive integers have exactly one integer 18 Aug 2025, 17:56
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Thaks Bunuel. As I read it again, it makes sense

Bunuel
MegB07
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

Hello, i didn't understand the language the 'The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?'

This means the largest number in the set? Please help.

We are told that two sets of four consecutive integers have exactly one integer in common. Because the sets are consecutive and share only one integer, it must be that the largest number of the smaller set equals the smallest number of the larger set.

The question then asks: how much greater is the sum of the set with larger numbers than the sum of the smaller set.

Example:

  • Smaller set: 1, 2, 3, 4
  • Larger set: 4, 5, 6, 7

The “set with greater numbers” is 4, 5, 6, 7.

So the problem is simply comparing the sum of the larger set with the sum of the smaller set, not the largest individual element.
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