AccelePrep for the ACT Test 2nd Edition Student Text

90 • S URGE TO S UCCESS ! M ATH T EST P REP

ANSWERS

1. (C) Mathematics/Number and Quantity/Rates and Proportions Preview the question. The item stem asks for the number of bags inspected by hand out of 10,000 „ƒ‰•ǡ •‘ –Š‹• ‹• ƒ ’”‘’‘”–‹‘ ’”‘„Ž‡Ǥ –ǯ• ƒ ‡ƒ•› problem, so the direct approach is probably the ˆƒ•–‡•–Ǥ •‡ ›‘—”…ƒŽ…—Žƒ–‘” ˆ‘” –Š‡ ƒ”‹–Š‡–‹…Ǥ Strategize and solve. ‡– —’ ƒ †‹”‡…– ’”‘’‘”–‹‘ „‡–™‡‡ –™‘ ”ƒ–‹‘• –‘ ϐ‹† –Š‡ —„‡” ‹•’‡…–‡† out of the total number: , x 750 9 10 000 Ǥ Use your calculator for the arithmetic: ( ) x 9 10000 750 120 # ' Ǥ Check your answer. The number of inspected „ƒ‰• ‘—– ‘ˆ ͳͲǡͲͲͲ ‹• ͳʹͲǡ ȋ ȌǤ 2. (H) Mathematics/Number and Quantity/ Properties of Numbers Preview the question Ǥ Š‡ ‹–‡ •–‡ ƒ•• ˆ‘” –Š‡ largest ‘ˆ ϐ‹˜‡…‘•‡…—–‹˜‡ ‘†† integers that total ͸ͺͷǤ •‡ ›‘—”…ƒŽ…—Žƒ–‘” ‘ –Š‹• ‹–‡Ǥ Strategize and solve Ǥ …ƒŽ…—Žƒ–‘” ‡ƒ• –Šƒ– ›‘— …ƒ –‡•–Ǧ–Š‡Ǧ–‡•– “—‹…Ž› ‘ –Š‹• ‹–‡Ǥ –ƒ”– ™‹–Š ȋ Ȍǣ ‹ˆ ͳ͵͹ ‹• –Š‡ Žƒ”‰‡•– ‘ˆ –Š‡ ϐ‹˜‡…‘•‡…—–‹˜‡ ‘†† ‹–‡‰‡”•ǡ –Š‡ ”‡ƒ‹†‡” ‹…Ž—†‡• ͳ͵ͷǡ ͳ͵͵ǡ ͳ͵ͳǡ ͳʹͻǣ 137 135 133 131 129 665 , ™Š‹…Š ‹• Ž‡•• –Šƒ –Š‡ ‰‹˜‡ •— ͸ͺͷǤ ‡•– –Š‡ ‡š– Žƒ”‰‡•– ˜ƒŽ—‡ǡ ͳͶͳǣ 141 139 137 135 133 685 , which ƒ–…Š‡• –Š‡ •— ͸ͺͷǤ This approach is easier, and probably ˆƒ•–‡”ǡ –Šƒ –Š‡ ƒŽ‰‡„”ƒ •‘Ž—–‹‘Ǥ ”ƒ•Žƒ–‡ –Š‡ ‰‹˜‡ ‹ˆ‘”ƒ–‹‘ ‹–‘ ƒ ‡“—ƒ–‹‘ ƒ† •‘Ž˜‡ ˆ‘” –Š‡ Žƒ”‰‡•– ‘†† ‹–‡‰‡”ǣ & ( ) ( ) ( ) ( ) n n n n n 2 685 4 6 8 & ( ) 5 685 2 4 6 8 n ( ) n 685 20 5 133 ' Ǥ Š‡ Žƒ”‰‡•– ‘ˆ –Š‡ integers is n 8 133 8 141 . Check your answer Ǥ Š‡ Žƒ”‰‡•– ‹–‡‰‡” ‹• ͳͶͳǡ •‘ –Š‡ ƒ•™‡” ‹• ȋ ȌǤ

3. (D) Mathematics/Number and Quantity/Basic Arithmetic Manipulations Preview the question. The item stem asks for the difference between two rational expressions ™‹–Š ‡š’‘‡–• ‘ˆ „ƒ•‡ ͳͲ ‹ ‡ƒ…Š †‡‘‹ƒ–‘”Ǥ Strategize and solve Ǥ ˆ ›‘— ƒ”‡…‘ˆ‘”–ƒ„Ž‡ working with exponents, simplify the expression: 10 1 10 1 10 1 10 10 10 1 10 10 10 1 25 26 25 26 26 26 d n If you are not comfortable with the rules of ‡š’‘‡–•ǡ —•‡ ›‘—”…ƒŽ…—Žƒ–‘”Ǩ ‘— ƒ› ‡˜‡ use it simply because it may be a faster method, †‡’‡†‹‰ ‘ –Š‡…ƒŽ…—Žƒ–‘”Ǥ Š‹…Š‡˜‡” ‡–Š‘† is fastest and less prone to error is the one you •Š‘—Ž†…Š‘‘•‡Ǥ ‘™ ˆ”ƒ…–‹‘• ƒ† ‡š’‘‡–• are entered in a calculator depends on the calculator—make sure you are familiar with ›‘—”• ƒ† –Š‡ ”‡“—‹”‡† ‘”†‡” ‘ˆ ‡› ‡–”‹‡•Ǥ Š‡ ϐ‹ƒŽ ”‡ƒ†‘—– •Š‘—Ž† „‡ 9 26 or 9E-26, which is the same as 9 10 26 # Ǥ Check your answer Ǥ ‘‡ ‘ˆ –Š‡ ƒ•™‡”• Šƒ˜‡ –Š‡ ˆ‘”ƒ– ‘ˆ ‡‰ƒ–‹˜‡ ‡š’‘‡–•ǡ •‘ ”‡™”‹–‡ 9 10 26 # with the exponent on the bottom: 9 10 10 9 26 26 # Ǥ Š‹• ˆ‘” ‘™ ƒ–…Š‡• choice ȋ ȌǤ 4. (J) Mathematics/Number and Quantity/ Properties of Numbers Preview the question. The item stem states that x ‹• •‘‡ ‡‰ƒ–‹˜‡ ˜ƒŽ—‡ „‡–™‡‡ 1 and 0, which makes x ƒ ‡‰ƒ–‹˜‡ ˆ”ƒ…–‹‘Ǥ Š‡”‡ ƒ”‡ –™‘ approaches to this problem: reason based on –Š‡ ’”‘’‡”–‹‡• ‘ˆ ‡‰ƒ–‹˜‡ ˆ”ƒ…–‹‘• ‘” —•‡ –Š‡ •–”ƒ–‡‰› ‘ˆ ’Ž—‰Ǧƒ†Ǧ…Š—‰Ǥ •‡ –Š‡ ‡–Š‘† –Šƒ– ‹• ˆƒ•–‡•– ƒ† Ž‡ƒ•– ‡””‘” ’”‘‡ ˆ‘” ›‘—Ǥ Strategize and solve. You can reason through –Š‡ ’”‘„Ž‡ ƒ ƒ•™‡”…Š‘‹…‡ ƒ– ƒ –‹‡Ǥ ȋ Ȍ ”‡’”‡•‡–• –Š‡ ˜ƒ”‹ƒ„Ž‡ ‹ < < 1 0 x , so 10 9 . 26