There are four unequal integers such that the difference of first two is 6…
2023
There are four unequal integers such that the difference of first two is 6 more than the sum of the next two numbers and sum of the first two is 3 less than the difference of next two , then what will be the value of difference of first and third ?
- A.
3.5
- B.
2
- C.
1.5
- D.
7
Attempted by 3 students.
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Correct answer: C
Let a, b, c and d be the four unequal numbers. We need to find a - c.
From the statement "the difference of the first two is 6 more than the sum of the next two":
a - b = 6 + (c + d).
Rearrange to combine a and c terms: (a - c) - (b + d) = 6, so
b + d = (a - c) - 6. (Equation 1)
From the statement "the sum of the first two is 3 less than the difference of the next two":
a + b = (c - d) - 3.
Rearrange: (c - a) - (b + d) = 3, so
b + d = (c - a) - 3. (Equation 2)
Equate the two expressions for b + d from Equation 1 and Equation 2:
(a - c) - 6 = (c - a) - 3.
Note that c - a = -(a - c). Substitute:
(a - c) - 6 = -(a - c) - 3.
Bring like terms together: 2(a - c) = 3.
Therefore a - c = 3/2 = 1.5.
Remark: The value 1.5 is not an integer, so the original phrase "four unequal integers" is inconsistent with the given relations. Interpreting the numbers as real numbers yields a - c = 1.5.