The ratio of the number of Jackie's pink T-shirts to the number of her purple T-shirts is 4:3. Which of the following cannot be the total number of her pink and purple T-shirts?

(A) 28 (B) 42 (C) 70 (D) 48

With one: A, B, C or D?

(D) 48

Step-by-step explanation:

Given,

The ratio of the number of Jackie's pink T-shirts to the number of her purple T-shirts = 4:3

Let pink T-shirts = 4x, purple shirts = 3x

Where,

x is any positive real numbers,

So, the total number of her pink and purple T-shirts = 4x + 3x = 7x

Since, 7x is the multiple of 7,

28, 42 and 70 are the multiple of 7,

So, they can be the total number of shirts,

But, 48 is not the multiple of 7,

Hence, 48 can not be the total number of her pink and purple T-shirts.

Since the number of T-shirts must be a whole number (she cannot use half a t-shirt), the total number must be a multiple of 7 (at least 4 pink t-shirts + 3 purple t-shirts must exist). The only answer choice which is not a multiple of 7 is D) 48.