How to find consecutive integers - SSAT Upper Level: Quantitative

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.

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.

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

, and they can be found using the equation

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

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

, and they can be found using the equation

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

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

,

and they can be found using the equation

The integers are 836, 837, 838, 839.

To get the correct response, multiply:

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

, and they can be found using the equation

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

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 .

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

, and they can be found using the equation

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

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.

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.

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

, and they can be found using the equation

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

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

, and they can be found using the equation

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

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

,

and they can be found using the equation

The integers are 836, 837, 838, 839.

To get the correct response, multiply:

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

, and they can be found using the equation

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

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 .

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.

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.

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

, and they can be found using the equation

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

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

, and they can be found using the equation

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

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

, and they can be found using the equation

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

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

,

and they can be found using the equation

The integers are 836, 837, 838, 839.

To get the correct response, multiply:

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

, and they can be found using the equation

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