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1. Which of the following could be a value of x, in the diagram above?
A. 10
B. 20
C. 40
D. 50
E. any of the above
Correct Answer: B
Explanation:
The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB. Also ABC is not a straight line and must be less than 180. Therefore 90 < 5x < 180 The only value of x which satisfies this relation is 20.
2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
A. 10
B. 15
C. 20
D. 25
E. 30
Correct Answer: A
Explanation:
20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.
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