Select all true answers and no false answers from the choice

Select all true answers, and no false answers, from the choices below.

Set up: in a box there are 6 ping-pong balls, each either purple or yellow, and marked with numbers as follows:

Yellow balls: 2, 6, 9

Purple balls: 0, 3, 7

Question 4 options:

( yellow balls y) ( purple ball x) such that the sum of the numbers on x and y is 9.

( purple ball y) such that ( yellow balls x) the number on y is greater than the number on x.

( purple ball x) such that ( yellow balls y) the sum of the numbers on x and y is at least 9.

( purple balls x) ( yellow ball y) such that the number on x is greater than the number on y.

There is a colour C such that there is a ball of colour C which has a number double the number on a certain ball of the other colour.

Solution

The correct statements are a,c,e

The first statement is true

Since for ball 2(in yellow), there exists 7(in purple)

Since for ball 6(in yellow), there exists 3(in purple)

Since for ball 9(in yellow), there exists 0(in purple)

The second statement is false

Since the largest of purple balls is 7, but there exists a yellow ball with number 9 which is greater than the purple ball

The third statement is true

Since there exists a purple ball with number 7, so adding with the balls in the yellow basket

we get 7 + 2 = 9, 7 + 6 = 13 and 7 + 9 =16

The fourth statement is false

since purple ballscontains 0 and there is no ball with number less than 0 in yellow balls

The fifth statement is true

since there is yellow ball with number 6 which is double of the purple ball with number 3