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Problem solving 1

Harriet wants to put up fencing around three sides of her rectangular yard and leave a side of 20 feet unfenced. If the yard has an area of 680 square feet, how many feet of fencing does she need? | 6 Harriet wants to put up fencing around three sides of her rectangular yard and leave a side of 20 feet unfenced. If the yard has an area of 680 square feet how many feet of fencing does she need A 34 B 40 C 68 88 E 102 w Proposed The diagram above shows the rectangular yard with the known dimension 20 feet and the unknown dimension w feet The area of the yard is 20iv - 680 square feet 680 so w 34 feet The length of fencing needed is then 34 20 34 88 feet Thus the best answer is D 7 If u t r q s t and t r which of the following must be true9 I u s IL s q III u r A I only B II only C III only II I and II E II and HI k s9 s 8 Increasing the original pace of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by A 32.25 B 31.00 C 30 25 D 30 00 E 22.50 If p is the original pnce then the 15 percent increase m pnce results in a pnce of 1 15 The next 15 percent increase in price results m a pnce of 1 15 1 15p or 1 3225 1 Thus the pnce increased by 1 3225p - p 0 3225 or 32 25 of p The best answer is A J 9 If k is an integer and O.OOj lQ x 10 is greater than 1 000 what is the least possible value of k A 2 B 3 C 4 D 5 E 6 Smix 0 0010101 is being multiplied by the fcth power of 10 k is the number of decimal places that the decimal point in 0 0010101 will move to the right if k 0 in the product 0 0010101 x 10 By inspection 6 is the least number of decimal places that the decimal point must move to the nght in order for the product to be greater than 1 000 Thus the best answer is E 10. If A-3 4 7 0apdh 3 thenh-v b J A -8 The number hne shown above is based bn the given inequalities and may be helpful when I II and III are considered I It may be that q 0 r 1 i 2 n 3 and s 4 so tfiat u s is not necessarily true II Since s t t r and r q it follows that s q HI Since u t and t r it follows that u r Since H and HI must be true the best answer is E - B -2 C . z 1 D - E 2 Since b - 3 1 4 - 0 it follows that either b -