Q: The ratio of the number of plants that Keisha has to the number of plants Sam has is 1:5. After Sam gives Keisha 5 plants, the ratio of plants Keisha has to the plants Sam has will be 2:7. How many more plants will Sam have than Keisha after 5 plants are given?

(Target Audience: GMAT)

1. 30
2. 45
3. 50
4. 60
5. 75

Explanation: Generic Way

Let K = # of plants that Keisha PRESENTLY has

Let S = # of plants that Sam PRESENTLY has

The ratio of the number of plants that Keisha has to the number of plants Sam has is 1:5

We can write: K/S = 1/5

Cross multiply to get: 5K = S

After Sam gives Keisha 5 plants, the ratio of plants Keisha has to the plants Sam has will be 2:7

After Sam gives Keisha 5 plants, we have

K + 5 = # of plants Keisha has

S – 5 = # of plants Sam has

So, we can write: (K +5)/(S – 5) = 2/7

Cross multiply to get: 7(K + 5) = 2(S – 5)

Expand: 7K + 35 = 2S – 10

Simplify: 7K – 2S = -45

We now have two equations with 2 variables:

5k = S

7K – 2S = -45

Take bottom equation and replace S with 5K to get: 7K – 2(5K) = -45

Simplify: -3K = -45

Solve: K = 15

So, Keisha PRESENTLY has 15 plants, which means Sam PRESENTLY has 75 plants

After Sam gives Keisha 5 plants, Keisha has 20 plants and Sam has 70 plants

How many more plants will Sam have than Keisha after 5 plants are given?

70 – 20 = 50

OPTION C

Explanation: HolaMaven Way

The easiest number to work with is 50

Question is asking number of extra plants Sam has after the giving and taking process is done.

Using Option C

if 50 extra plants, then number of plants each of them has is 20 and 70 (2:7 ratio)

Now since Sam has given 5 plants to Keisha,

plants available to both of them before exchange is 70+5 = 75 and 20-5 = 15 respectively

Ratio of 15 and 75 is 1:5, which is matching the condition in question.