SSAT Upper Level Quantitative - How to find consecutive integers

What is the value of is this sequence?

Explanation

This is a geometric sequence since the pattern of the sequence is through multiplication.

You have to multiple each value by to get the next one.

The value before is so .

Three consecutive integers have sum . What is their product?

$\text{No three consecutive integers have sum } 427.$

Explanation

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-1 \right )+ x +\left ( x+1 \right ) = 427$

$x = 142\frac{1}{3}$

This contradicts the condition that the numbers are integers. Therefore, three integers satisfying the given conditions cannot exist.

Which of the following can be the sum of four consecutive positive integers?

None of the other answers are correct.

Explanation

Let , , , and be the four consecutive integers. Then their sum would be

In other words, if 6 were to be subtracted from their sum, the difference would be a multiple of 4. Therefore, we subtract 6 from each of the choices and see if any of the resulting differences are multiples of 4.

$178 -6 = 172 ; 172 \div4 = 43$

$213 -6 = 207 ; 207 \div4 = 51 ; R ; 3$

$420 -6 = 414 ; 414 \div4 = 103 : R : 2$

$143 -6 = 137 ; 137 \div4 = 34: R: 1$

Since this only happens in the case of 178, this is the only number of the four that can be a sum of four consecutive integers: 43, 44, 45, 46.

Three consecutive odd integers have sum 537. What is the product of the least and greatest of the three?

$32\textup{,}037$

$29\textup{,}237$

$29\textup{,}925$

$30\textup{,}621$

$31\textup{,}325$

Explanation

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-2 \right )+ x +\left ( x+2 \right ) = 537$

The three integers are 177, 179, and 181, and the product of the least and greatest is

$177 \times 181 = 32,037$

Three consecutive integers have a sum of . What is their product?

$\text{No three consecutive integers have sum 312.}$

Explanation

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-1 \right )+ x +\left ( x+1 \right ) = 312$

The integers are therefore 103, 104, 105. The correct response is their product, which is

$103 \times 104 \times 105= 1,124,760$

Four consecutive integers have sum 3,350. What is the product of the middle two?

$701\textup{,}406$

$703\textup{,}082$

$704\textup{,}760$

$699\textup{,}732$

$\textup{No four consecutive integers have a sum of 3,350}$

Explanation

Call the least of the four integers . The four integers are therefore

and they can be found using the equation

$x + \left (x+1 \right )+\left (x+2 \right )+\left ( x+3 \right )= 3,350$

$x=3,344 \div 4 = 836$

The integers are 836, 837, 838, 839.

To get the correct response, multiply:

$837 \times 838 = 701,406$

Three consecutive even integers have sum 924. What is the product of the least and greatest of the three?

No three consecutive even integers have sum 924.

Explanation

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

$\left (x-2 \right )+ x +\left ( x+2 \right ) = 924$

The three even integers are therefore 306, 308, and 310, and the product of the least and greatest of these is

$306 \times 310= 94,860$

How to find consecutive integers

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