There are some red, blue and green buttons.

The ratio of the number of red buttons to the number of blue buttons is 4 : 1.

The ratio of the number of red buttons to the number of green buttons is 3 : 2.

There are 120 more red buttons than green buttons.

How many buttons are there altogether?

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

R : B = 4 : 1 and R : G = 3 : 2

The number of red buttons in both ratios are the same.

Jason had some apples and oranges in the ratio 5 : 4.

He sold 42 apples and the ratio of the number of apples to the number of oranges became 1 : 2.

How many apples did Jason have at first?

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

The number of oranges remain unchanged (the same).

The number of apples changed.

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

D : E = 5 : 8 and F : E = 1 : 2

The number of Eugene's stamps in both ratios are the same.

Box A and Box B had some paper clips in the ratio 5 : 9.

Mary took 32 paper clips from Box B and put them in Box A.

Both boxes then had the same number of paper clips.

How many paper clips were in Box A at first?

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

B --> A

Transfer between A and B only --> Total number of paper clips remain unchanged.

The ratio of Halimah’s red beads to blue beads was 2 : 3.

After she bought another 45 blue beads, the ratio of the number of red beads to the number of blue beads was 5 : 9.

How many more blue beads than red beads did she have at first?

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

The number of red beads remains unchanged (the same).

The number of blue beads changed.

Sanjay had some red buttons and pink buttons in the ratio 1 : 3.

She then bought 15 red and pink buttons each and the ratio became 2 : 5.

How many pink buttons did she have at first?

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

Red --> +15

Pink --> +15

Difference will remain unchanged.

10 years ago, the ratio of Marcy's age to Brenda's age was 2 : 5.

The difference in their ages was 9 years.

What is the ratio of Marcy's age to Brenda's age now?

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

The difference in age between two persons will always remain unchanged.

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

Children --> -120

Adults --> +120

The total number of people remains unchanged.

The ratio of the number of boys to the number of girls at a gathering was 2 : 5.

After 21 boys and 21 girls joined the gathering, the ratio became 3 : 4.

How many boys were there at first?

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

Boys --> + 21

Girls --> + 21

The difference between the number of boys and the number of girls remains unchanged.

• One Unchanged Quantity

• Unchanged Total

• Unchanged Difference

• Repeated Identity

Answer explanation

K+J is the repeated identity