The meaning of a prime number is a number that is divisible by only one and itself. A element number can"t be divided by zero, because numbers split by zero room undefined. The the smallest prime number is 2, i beg your pardon is likewise the only even prime.

**Correct answer:**

Explanation:

The third smallest prime number is 5. (Don"t forget that 2 is a prime number, yet 1 is not!)

The smallest 2 digit prime number is 11.

Now we have the right to evaluate the whole expression:

If ax + bx = c, whereby c is a element integer, and a and also b are hopeful integers which of the following is a feasible value the x?

Explanation:

This inquiry tests an easy number properties. Prime numbers are numbers which are divisible only by one and themselves. Answer options "2" and also "4" are automatically out, due to the fact that they will constantly produce even commodities with a and b, and the amount of two even assets is always even. Since no also number better than 2 is prime, 2 and also 4 can not be price options. 3 is tempting, until you remember that the sum of any type of two multiples that 3 is itself divisible through 3, thereby negating any possible answer because that c other than 3, i m sorry is impossible. There are, however, several feasible combinations that work with x = 1. For instance, a = 8 and also b = 9 means that 8(1) + 9(1) = 17, i beg your pardon is prime. You only need to find one instance to demonstrate that an alternative works. This eliminates the "None that the various other answers" alternative as well.

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### Example concern #81 : Arithmetic

Which declare is false around prime numbers?

**Possible Answers:**

Every positive integer except for 1 is a prime or a product that primes.

Every integer greater than 1 has actually a distinctive prime factorization.

There are no an adverse primes.

All are false.

None are false.

**Correct answer:**

None are false.

Explanation:

All of this statements space true. Let"s go with them.

1. There space no an adverse prime numbers. This appears as if it might be false, yet in fact, the element numbers room defined all at once numbers *greater* than one that space divisible by only one and itself.

2. Every number other than 0 and also 1 is a element number or product the primes. This is likewise true. Let"s look at the factorization of a number the isn"t prime. Because that example, 6 = 2 * 3, i beg your pardon is a product of primes. 12 = 2 * 2 * 3, i m sorry is additionally a product that primes.

3. Every number has actually a distinctive prime factorization. We simply saw the every number is one of two people prime, or a product of primes. As such each number must have a unique prime factorization. Simply as above, 6 is the product of two primes, 2 and 3. No various other number have the right to be make by mulitplying 2 * 3. The exact same is true for 12. When we multiply 2 * 2 * 3, the just number we will ever get is 12.

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### Example concern #82 : Arithmetic

Column A

5!/3!

Column B

6!/4!

**Possible Answers:**

The connection cannot be determined from the info given.

The amount in tower B is greater.

The two amounts are equal.

The quantity in column A is greater.

**Correct answer:**

The amount in shaft B is greater.

Explanation:

This is a straightforward factorial question. A factorial is equal to the number time every positive whole number smaller than itself. In column A, the molecule is 5 * 4 * 3 * 2 * 1 if the denominator is 3 * 2 * 1.

As you deserve to see, the 3 * 2 * 1 deserve to be cancelled out from both the numerator and also denominator, leaving only 5 * 4.

The value for shaft A is 5 * 4 = 20.

In shaft B, the numerator is 6 * 5 * 4 * 3 * 2 * 1 while the denominator is 4 * 3 * 2 * 1. After simplifying, tower B gives a worth of 6 * 5, or 30.

Thus, tower B is higher than shaft A.

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### Example inquiry #83 : Arithmetic

Which the the following integers are components of both 24 and 42?

**Possible Answers:**

3

8

12

7

5

**Correct answer:**3

Explanation:

3 is the only answer the is a element of both 24 and also 42. 42/3 = 14 and 24/3 = 8. The other answers are either a variable of 24 OR 42 or neither, however not both.

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### Example concern #84 : Arithmetic

721(413) + 211(721) is same to i beg your pardon of the following?

**Possible Answers:**

413(721 + 211)

211(413 + 721)

(721 + 413)(211 +721)

721(413 + 211)

(721 + 211)(413 + 721)

**Correct answer:**

721(413 + 211)

Explanation:

The price is 721(413 + 211) since we deserve to pull the end a typical factor, or 721, native both sides of the equation.

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### Example concern #85 : Arithmetic

*n* is a hopeful integer
. *p* = 4 * 6 * 11 * n

Quantity A: The remainder when *p* is split by 5

Quantity B: The remainder when *p* is split by 33

**Possible Answers:**

Quantity A is greater.

Quantity B is greater.

The relationship cannot be identified from the information given.

The two amounts are equal.

**Correct answer:**

The relationship cannot be identified from the details given.

Explanation:

Let"s take into consideration Quantity B first. What will the remainder be when *p* is divided by 33?

4, 6 and also 11 are factors of *p* which means that 2 * 2 * 2 * 3 * 11 * *n* will equal *p*. Us can team the 3 and also 11 to view that 33 will constantly be a variable of *p* and also will have no remainder. For this reason Quantity B will constantly equal 0 no issue the worth of *n*.

Now consider Quantity A. Let"s consider very first the worths for *p* once n amounts to 1 through 5. Once *n* = 1, *p* = 264, and the remainder is 4/5 or 0.8.

*n* = 2, *p* = 528, and also the remainder is 3/5 or 0.6.

*n* = 3, *p* = 792, and the remainder is 2/5 or 0.4.

*n* = 4, *p* = 1056, and also the remainder is 1/5 or 0.2.

*n* = 5, *p* = 1320, and the remainder is 0 (because when *n* = 5, 5 i do not care a variable of *p* and also thus over there is no remainder.

Because amount A have the right to be equal to or better than B, there is not enough information given to identify the relationship.

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### Example concern #86 : Arithmetic

Quantitative Comparison

Quantity A: number of 2"s in the element factorization that 32

Quantity B: number of 2"s in the element factorization that 60

**Possible Answers:**

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

**Correct answer:**

Quantity A is greater.

Explanation:

32 = 2 * 16 = 2 * 4 * 4 = 2 * 2 * 2 * 2 * 2 = 25, so quantity A = 5.

60 = 2 * 30 = 2 * 6 * 5 = 2 * 2 * 3 * 5 = 22 * 3 * 5, so amount B = 2.

Quantity A is greater. Also though 60 is a bigger number than 32, 32 has much more 2"s in its prime factorization.

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### Example concern #87 : Arithmetic

If

is one integer and also is one integer, i beg your pardon of the following could be the value of ?**Possible Answers:**

**Correct answer:**

Explanation:

Because

, the answer choice that has a factorization set that cancels out totally with 396 will produce an integer. Just 18 fits this qualification, because .See more: What Is An Iris Diaphragm On A Microscope, Compound Microscope Parts

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