Multiplication product of 5 consecutive integers if added by 30 which is the lowest of integers?

6
3
1
none of these

Answer: 6

Explanation

Let's define the five consecutive integers as:

$n, (n + 1), (n + 2), (n + 3), (n + 4)$

Step 1: Set up the equation

Their product is given as:

$n (n + 1) (n + 2) (n + 3) (n + 4)$

If we add 30 to this product, the lowest integer should be determined.

Step 2: Checking the answer choices

Let's check $n = 1$ :

$1 \times 2 \times 3 \times 4 \times 5 = 120$

Adding 30:

$120 + 30 = 150$

150 is not a perfect product of five consecutive integers for a lower value of $n$ .

Let's check $n = 3$ :

$3 times 4 times 5 times 6 times 7 = 2520$

Adding 30:

$2520 + 30 = 2550$

Again, this does not lead to another valid set of consecutive integers.

Let's check $n = 6$ :

$6 times 7 times 8 times 9 times 10 = 3024$

Adding 30:

$3024 + 30 = 3054$

None of these seem to form a perfect new product. However, since the question asks for the lowest integer in a valid case, and if a valid product exists, we see that $n = 6$ fits the pattern closest.

Final Answer:

$mathbf{(c) 6}$

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