How to add integers - SAT Math

Card 0 of 40

Question

Find the values of the variables and in the following sequence:

Answer

Terms are obtained by alternately adding 5 and multiplying by 3:

$11\times 3 = 33$

$38 \times 3 = 114$

The missing two elements are found by multiplying by 3, then by adding 5:

$A=119 \times 3 = \underline{357}$

$B=357 + 5 = \underline{362}$

Multiplying by 3 confirms that this is correct:

$362 \times 3 = 1086$

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Question

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

Answer

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

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Question

What is the sum of multiples of 10 from 10 to 140 inclusive?

Answer

Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.

Compare your answer with the correct one above

Question

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.

Answer

After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.

Observe the operations as carried out with 2:

$6 \times 2 =12$

$10 \div 2 = 5$

Carrying out the same steps, in order, with 4:

$9 \times 4 = 36$

$32 \div 4 = 8$

Carrying out the same steps, in order, with 6:

$14 \times 6 = 84$ , the number that replaces the circle;

$84 - 6 = \underline{78}$ , the number that replaces the square.

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Question

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

Answer

To solve this problem. First set up a mathematical equation that represents this scenario.

"The sum of three consecutive even numbers is 42."

Let

$x=\text{beginning number in the sequence}$

and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes

$\x+(x+2)+((x+2)+2)=42 \x+x+2+x+4=42 \3x+6=42$

From here isolate the variable on one side of the equations with all other constants on the other side.

Subtract six from both sides.

$\3x+6{\color{Red} -6}=42{\color{Red} -6} \3x=36$

Now divide by three.

$\\frac{3x}{3}=\frac{36}{3} \\x=\frac{12\cdot 3}{3} \\x=12$

Since represents the beginning number in this sequence it also represents the smallest even number in this sequence. Therefore the smallest even number is 12.

Compare your answer with the correct one above

Question

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

Answer

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

Compare your answer with the correct one above

Question

What is the sum of multiples of 10 from 10 to 140 inclusive?

Answer

Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.

Compare your answer with the correct one above

Question

Find the values of the variables and in the following sequence:

Answer

Terms are obtained by alternately adding 5 and multiplying by 3:

$11\times 3 = 33$

$38 \times 3 = 114$

The missing two elements are found by multiplying by 3, then by adding 5:

$A=119 \times 3 = \underline{357}$

$B=357 + 5 = \underline{362}$

Multiplying by 3 confirms that this is correct:

$362 \times 3 = 1086$

Compare your answer with the correct one above

Question

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.

Answer

After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.

Observe the operations as carried out with 2:

$6 \times 2 =12$

$10 \div 2 = 5$

Carrying out the same steps, in order, with 4:

$9 \times 4 = 36$

$32 \div 4 = 8$

Carrying out the same steps, in order, with 6:

$14 \times 6 = 84$ , the number that replaces the circle;

$84 - 6 = \underline{78}$ , the number that replaces the square.

Compare your answer with the correct one above

Question

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

Answer

To solve this problem. First set up a mathematical equation that represents this scenario.

"The sum of three consecutive even numbers is 42."

Let

$x=\text{beginning number in the sequence}$

and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes

$\x+(x+2)+((x+2)+2)=42 \x+x+2+x+4=42 \3x+6=42$

From here isolate the variable on one side of the equations with all other constants on the other side.

Subtract six from both sides.

$\3x+6{\color{Red} -6}=42{\color{Red} -6} \3x=36$

Now divide by three.

$\\frac{3x}{3}=\frac{36}{3} \\x=\frac{12\cdot 3}{3} \\x=12$

Since represents the beginning number in this sequence it also represents the smallest even number in this sequence. Therefore the smallest even number is 12.

Compare your answer with the correct one above

Question

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

Answer

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

Compare your answer with the correct one above

Question

What is the sum of multiples of 10 from 10 to 140 inclusive?

Answer

Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.

Compare your answer with the correct one above

Question

Find the values of the variables and in the following sequence:

Answer

Terms are obtained by alternately adding 5 and multiplying by 3:

$11\times 3 = 33$

$38 \times 3 = 114$

The missing two elements are found by multiplying by 3, then by adding 5:

$A=119 \times 3 = \underline{357}$

$B=357 + 5 = \underline{362}$

Multiplying by 3 confirms that this is correct:

$362 \times 3 = 1086$

Compare your answer with the correct one above

Question

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.

Answer

After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.

Observe the operations as carried out with 2:

$6 \times 2 =12$

$10 \div 2 = 5$

Carrying out the same steps, in order, with 4:

$9 \times 4 = 36$

$32 \div 4 = 8$

Carrying out the same steps, in order, with 6:

$14 \times 6 = 84$ , the number that replaces the circle;

$84 - 6 = \underline{78}$ , the number that replaces the square.

Compare your answer with the correct one above

Question

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

Answer

To solve this problem. First set up a mathematical equation that represents this scenario.

"The sum of three consecutive even numbers is 42."

Let

$x=\text{beginning number in the sequence}$

and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes

$\x+(x+2)+((x+2)+2)=42 \x+x+2+x+4=42 \3x+6=42$

From here isolate the variable on one side of the equations with all other constants on the other side.

Subtract six from both sides.

$\3x+6{\color{Red} -6}=42{\color{Red} -6} \3x=36$

Now divide by three.

$\\frac{3x}{3}=\frac{36}{3} \\x=\frac{12\cdot 3}{3} \\x=12$

Since represents the beginning number in this sequence it also represents the smallest even number in this sequence. Therefore the smallest even number is 12.

Compare your answer with the correct one above

Question

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

Answer

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

Compare your answer with the correct one above

Question

What is the sum of multiples of 10 from 10 to 140 inclusive?

Answer

Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.

Compare your answer with the correct one above

Question

Find the values of the variables and in the following sequence:

Answer

Terms are obtained by alternately adding 5 and multiplying by 3:

$11\times 3 = 33$

$38 \times 3 = 114$

The missing two elements are found by multiplying by 3, then by adding 5:

$A=119 \times 3 = \underline{357}$

$B=357 + 5 = \underline{362}$

Multiplying by 3 confirms that this is correct:

$362 \times 3 = 1086$

Compare your answer with the correct one above

Question

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.

Answer

After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.

Observe the operations as carried out with 2:

$6 \times 2 =12$

$10 \div 2 = 5$

Carrying out the same steps, in order, with 4:

$9 \times 4 = 36$

$32 \div 4 = 8$

Carrying out the same steps, in order, with 6:

$14 \times 6 = 84$ , the number that replaces the circle;

$84 - 6 = \underline{78}$ , the number that replaces the square.

Compare your answer with the correct one above

Question

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

Answer

To solve this problem. First set up a mathematical equation that represents this scenario.

"The sum of three consecutive even numbers is 42."

Let

$x=\text{beginning number in the sequence}$

and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes

$\x+(x+2)+((x+2)+2)=42 \x+x+2+x+4=42 \3x+6=42$

From here isolate the variable on one side of the equations with all other constants on the other side.

Subtract six from both sides.

$\3x+6{\color{Red} -6}=42{\color{Red} -6} \3x=36$

Now divide by three.

$\\frac{3x}{3}=\frac{36}{3} \\x=\frac{12\cdot 3}{3} \\x=12$

Since represents the beginning number in this sequence it also represents the smallest even number in this sequence. Therefore the smallest even number is 12.

Compare your answer with the correct one above

Tap the card to reveal the answer

How to add integers - SAT Math

Find the values of the variables and in the following sequence:

Terms are obtained by alternately adding 5 and multiplying by 3: The missing two elements are found by multiplying by 3, then by adding 5: Multiplying by 3 confirms that this is correct:

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

What is the sum of multiples of 10 from 10 to 140 inclusive?

Examine the sequence: Give the number that replaces the square.

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

What is the sum of multiples of 10 from 10 to 140 inclusive?

Find the values of the variables and in the following sequence:

Terms are obtained by alternately adding 5 and multiplying by 3: The missing two elements are found by multiplying by 3, then by adding 5: Multiplying by 3 confirms that this is correct:

Examine the sequence: Give the number that replaces the square.

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

What is the sum of multiples of 10 from 10 to 140 inclusive?

Find the values of the variables and in the following sequence:

Terms are obtained by alternately adding 5 and multiplying by 3: The missing two elements are found by multiplying by 3, then by adding 5: Multiplying by 3 confirms that this is correct:

Examine the sequence: Give the number that replaces the square.

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

What is the sum of multiples of 10 from 10 to 140 inclusive?

Find the values of the variables and in the following sequence:

Terms are obtained by alternately adding 5 and multiplying by 3: The missing two elements are found by multiplying by 3, then by adding 5: Multiplying by 3 confirms that this is correct:

Examine the sequence: Give the number that replaces the square.

The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.

Examine the sequence:

$4, 6, 12 ,10, 5 ,9, 36, 32, 8, 14, \bigcirc, \square, ...$

Give the number that replaces the square.