Divisibility/factors

[BTGmoderatorRO]

How many multiples of 5 are there between 81 and 358?
A. 54
B. 55
C. 56
D. 57
E. 58
i tried this formula $$sum\ =\ \frac{\left(a1+an\right)}{2}\cdot n$$
OA is b

what approach can i use to reach my destination happily? Thanks

[EconomistGMATTutor]

How many multiples of 5 are there between 81 and 358?
A. 54
B. 55
C. 56
D. 57
E. 58
i tried this formula sum = (a1+an)2â‹…n
sum = (a1+an)2â‹…n

OA is b

what approach can i use to reach my destination happily? Thanks

Hi Roland2rule,
Let's take a look at your question.
It's a bit tricky one.

We are asked to find the number of multiples of 5 between 81 and 358.
We know that first multiple of 5 between 81 and 358 will be 85 and the last one would be 355.
So why not write an arithmetic sequence of multiples of 5 starting from 85 for this, like:
$$85,\ 90,\ 95,\ ..,\ 355$$

Since this is a sequence of multiples of 5, so number of terms in this sequence will give us the number of multiples of 5 between 81 and 358.
We know that in an arithmetic sequence,
$$a_n=a_1+\left(n-1\right)d ... (i)$$

In the sequence given above,
$$a_1=85,\ a_n=355,\ d=5$$

Plugging in these values in eq (i),
$$355=85+\left(n-1\right)5$$
$$355-85=\left(n-1\right)5$$
$$270=\left(n-1\right)5$$
$$n-1=\frac{270}{5}$$
$$n-1=54$$
$$n=54+1$$
$$n=55$$

It means that the number of terms in this sequence is 55.
Therefore, the number of multiples between 81 and 358 is 55.

Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

[Scott@TargetTestPrep]

How many multiples of 5 are there between 81 and 358?
A. 54
B. 55
C. 56
D. 57
E. 58
i tried this formula $$sum\ =\ \frac{\left(a1+an\right)}{2}\cdot n$$
OA is b

what approach can i use to reach my destination happily? Thanks

The smallest multiple of 5 in the given interval is 85, and the greatest multiple of 5 is 355. Therefore, the number of multiples of 5 in the interval is:

(355 - 85)/5 + 1 = 55

Answer: B