Ratios, Averages, and Digit Sums

The video revisits problem 180, offering a simpler solution involving fractions and population calculations. Problem 181 explores ratios and data sufficiency, demonstrating that the ratio of increased quantities cannot be determined with given data. Problem 182 involves solving for z minus x using arithmetic means. Problem 183 calculates the fraction of air removed from a tank after multiple strokes. Finally, problem 184 examines sums of two-digit numbers with reversed digits, using deductive reasoning to identify impossible sums.

In a nationwide poll, if 1/4 of the people answered 'yes' to question one and 1/3 of those answered 'yes' to question two, what fraction of the total population said 'yes' to both questions?

• 1/8

• 1/16

• 1/6

• 1/12

Tags

CCSS.6.RP.A.3A

If the ratio of two quantities is 3:4 and each is increased by 5, what can be said about the new ratio?

• It becomes 8:9

• It remains 3:4

• It becomes 4:5

• It cannot be determined

Tags

CCSS.6.RP.A.3A

What is the new ratio when two quantities in the ratio 3:4 are both increased by 5?

• 3:4

• Cannot be determined

• 8:9

• 4:5

Tags

CCSS.7.EE.B.3

Given that the average of x and y is 60, and the average of y and z is 80, what is the value of z - x?

• 50

• 40

• 30

• 20

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

If half of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original air is left after four strokes?

• 1/16

• 1/2

• 1/8

• 1/4

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

After four strokes of a vacuum pump, what fraction of the original air has been removed from the tank?

• 1/2

• 7/8

• 15/16

• 3/4

Tags

CCSS.5.NF.B.5B

If 1/2 of the air is removed with each stroke, how much air is left after three strokes?

• 1/16

• 1/8

• 1/2

• 1/4

Tags

CCSS.3.OA.D.9

If two-digit integers M and N have the same digits in reverse order, which of the following cannot be their sum?

• 121

• 165

• 181

• 99

Tags

CCSS.1.NBT.C.4

CCSS.2.NBT.B.5

For two-digit numbers with reversed digits, if the sum of the digits is less than 10, what can be said about the sum of the numbers?

• It has repeated digits

• It is less than 100

• It is a palindrome

• It is always even

Tags

CCSS.3.OA.D.9

If the sum of the digits of two reversed two-digit numbers is greater than 10, what is true about the tens and ones digits of their sum?

• Sum is a palindrome

• Ones digit is one more than tens digit

• Tens digit is one more than ones digit

• Both digits are equal

Tags

CCSS.3.OA.D.9