Question

What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?
19900
19533
19522
19534

Answer 1

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Only number that has exactly one factor is 1

Which numbers have exactly 2 factors?

This would be the list of prime numbers

Which numbers have more than 2 factors?

All composite numbers have more than 2 factors.

Which numbers have exactly 3 factors?

Squares of prime numbers have exactly 3 factors.

Sum of all numbers either prime or have more than 3 factors can be obtained by

Sum of all natural numbers less than 200 - Sum of numbers with 1 or 3 factors.

Numbers with 1 or 3 factors = 1, 4, 9, 25, 49, 121, 169

Sum of remaining numbers = (1 + 2 + 3 + 4 + 5 …..199)

– (1 + 4 + 9 + 25 + 49 + 121 + 169)

= 19900 - 378 = 19522

$\mathscr{ANSWER}$- Option C, 19522

Answer 2

Answer:

I'm either not understanding the question correctly, or there is a problem with it. When the price is $150, the merchant makes $15,000. If he raises the price slightly he will make roughly that amount, so D and E are the only reasonable answers (A, B and C are far too small). But we can see that if he raises the price 4%, to $156, he will sell 97 items. His revenue will be 156*97 dollars. That's an even number, but answers D and E will both be odd numbers if you plug in x = 156. So none of the answer choices could be right.

It's unclear to me exactly what the question is asking, because it's not clear if the percent increase described is meant to compound. Assuming it is not, then since 4% of $150 is $6, when the price increases by $6, the vendor sells 3 fewer items.

We're told the price is $x. The number of items sold will be 100 - 3*(x - 150)/6 = 100 - (x-150)/2 = 175 - (x/2).

Multiplying number of items by price, we get revenue:

x(175 - x/2) = 175x - x^2/2

so that should be the answer, unless I've misunderstood what the question is trying to say.

Note also that if the sales drop by 3 for every $6 increase in price, so drop by 1 for every $2 increase in price, we should expect the revenue to be $0 when the price is $350 (because if the price rises by $200, sales drop by 100, so sales drop to zero). So we should expect something like (350 - x) or (175 - x/2) to be a factor of the correct answer here, a fact one might be able to use to avoid doing all the work above.