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Re: On the first of the year, James invested x dollars at Proudstar bank in an account that yields

There are several issues with the question. For one thing ,we don't know if the interest on the first account is simple interest or compound interest. If the account earns 2% simple interest every quarter year, it will earn 8% interest in a full year, and the answer is C. If instead the interest com...

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Re: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than

The root of each answer choice is less than 10, so we're looking for an answer choice which has distinct prime factors that multiply to something less than 10. But the only two distinct primes that multiply to something less than 10 are 2 and 3, so we want the answer that is only divisible by 2 and ...

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Re: A company will select 2 of the 6 candidates available to work in 2 different positions in

The wording isn't clear enough, but if the two Tech positions are different (e.g. one is a Manager and the other an Engineer), then order matters, and we'll have 6 choices for the first position, 5 for the second, and 6*5 = 30 choices in total. If the HR positions are the same, order doesn't matter,...

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Re: A shopkeeper offers two successive discounts of \(20\%\) each on a sweater and still makes a profit of \(60\%.\) By

When a price is reduced by 20%, it becomes 80%, or 0.8, of its original value. So if a price is discounted by 20% twice, it becomes (0.8)(0.8) = 0.64 of its original value. So if the pre-discount price of the sweater was $100, the post-discount price was $64. If the retailer still makes a 60% profit...

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Re: What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)

Gmat_mission wrote: ↑

Sun Nov 28, 2021 6:51 am

What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)

You can also replace "4" with "5 - 1", so the expression becomes

5 + (5-1)*5 + (5-1)*5^2 + (5-1)*5^3 + (5-1)*5^4 + (5-1)*5^5
= 5 - 5 + 5^2 - 5^2 + 5^3 - 5^3 + 5^4 - 5^4 + 5^5 - 5^5 + 5^6
= 5^6

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Re: A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?

The product of the digits will only be odd if all three digits are odd. If we want all of our digits to be odd, we'd have 5 choices for each digit, so there will be 5^3 = 125 such three-digit numbers. For the remaining 900 - 125 = 775 three-digit numbers, the product of the digits will be even. So i...

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Re: How many distinct prime divisors does a positive integer \(n\) have?

If n is a positive integer, 2n is clearly divisible by 2. If, as Statement 1 says, 2n has only one prime divisor, that prime divisor must be 2. But then n can be 1, 2, 2^2, 2^3 or any other power of 2. Since it is possible n = 1, it is possible n has no prime divisors, and if n is any other power of...

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Re: If \(N\) is the product of all integers from \(1\) to \(100,\) both inclusive, then what is the remainder when

Between 1 and 100, there are 14 multiples of 7 (since 7*14 = 98), so 100! is divisible by at least 7^14. But two of those multiples of 7, namely 49 and 98, are multiples of 7^2, so they give us one extra 7, and 100! is actually divisible by 7^16. So 100! is a multiple of 7^16, and 100! + 100 is thus...