AccelePrep for the ACT Test 2nd Edition Student Text

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

‘–‡†ǡ •‘ ›‘—…ƒ –”—•– –Š‡ ’”‘’‘”–‹‘• ‹ –Š‡ ϐ‹‰—”‡ǣ –Š‡ •Šƒ†‡† ƒ”‡ƒ looks about one-half of the entire rectangle, or 4 2 2 1 = Ǥ •–‹ƒ–‡ –Š‡ answer choices using 3 . r Ǥ ȋ Ȍ ‹• –Š‡…Ž‘•‡•–ǣ 2 2 2 2 3 2 1 . r Ǥ 4. Š‡ ™ƒ–• ›‘— –‘ ‰‡–…‘ˆ—•‡† „› –Š‡ ˜ƒ”‹ƒ„Ž‡ x Ǥ Š‹• ‹• ‘– ƒ Šƒ”† ‹–‡ǡ Œ—•– ’‘–‡–‹ƒŽŽ› ‘”‡…‘ˆ—•‹‰ ƒ† –‹‡Ǧ…‘•—‹‰Ǥ Š‡ –‘–ƒŽ ˜ƒŽ—‡ ‹• x x 10 6 5 dimes dime cents nickels nickel cents # # _ i x x x 10 5 30 15 30 …‡–•Ǥ •–‡ƒ†ǡ ƒ˜‘‹† –Š‡ ˜ƒ”‹ƒ„Ž‡•Ǥ ˆ –Š‡”‡ ™ƒ• ͳ †‹‡ǡ –Š‡”‡ ™‡”‡ 1 6 7 ‹…‡Ž•Ǥ Š‡ –‘–ƒŽ ˜ƒŽ—‡ ‹• ( ) ( ) 1 10 7 5 45 …‡–•Ǥ ‡•– –Š‡ ƒ•™‡” …Š‘‹…‡•Ǥ Ž› ȋ Ȍ ‡“—ƒŽ• Ͷͷǣ ( ) x 15 30 15 1 30 45 Ǥ 5. ‡’Žƒ…‡ –Š‡ ˜ƒ”‹ƒ„Ž‡ r ™‹–Š ƒ ˜ƒŽ—‡ǡ •ƒ› ʹǤ This makes the second ’”‘„Ž‡ —…Š ‡ƒ•‹‡” –‘ •‘Ž˜‡Ǥ ˜ƒŽ—ƒ–‡ –Š‡ expressions: ( ) 3 2 12 2 S S and ( ) 3 1 3 2 S S Ǥ ‹…‡ 12 r is four times as large as 3 r , the answer is ȋ ȌǤ 6. Š‡…‘””‡…– ƒ•™‡” ‹• –Š‡ ‘‡ –Šƒ– †‘‡•ǯ– ‡‡– –Š‡…‘†‹–‹‘•Ǥ Test each choice starting with the second condition: & m n m n 4 3 3 4 Ǥ ˆ 6 n , ( ) m 3 6 4 14 and m n 14 6 20 ǡ ™Š‹…Š ‹• †‹˜‹•‹„Ž‡ „› ͷǡ •‘ ‡Ž‹‹ƒ–‡ ȋ ȌǤ ˆ 8 n , ( ) m 3 8 4 20 and m n 20 8 28 , which is not †‹˜‹•‹„Ž‡ „› ͷǡ •‘ ȋ Ȍ —•– „‡ –Š‡ ƒ•™‡”Ǥ †‡‡†ǡ ͳͳǡ ȋ Ȍǡ ͳ͸ǡ ȋ Ȍǡ ƒ† ʹͳǡ ȋ Ȍǡ ƒ”‡ ƒŽŽ ’‘••‹„Ž‡ ˜ƒŽ—‡• ˆ‘” n: if 11 n , ( ) m 3 11 4 29 and m n 29 11 40 ǡ ™Š‹…Š ‹• †‹˜‹•‹„Ž‡ „› ͷǤ ˆ 16 n , ( ) m 3 16 4 44 and m n 44 16 60 ǡ ™Š‹…Š ‹• †‹˜‹•‹„Ž‡ „› ͷǤ And if 21 n , ( ) m 3 21 4 59 and m n 59 21 80 , which is †‹˜‹•‹„Ž‡ „› ͷǤ 7. If x is the original amount of the gift, after buying books, Cyd had ( ) x 4 3 Ž‡ˆ–Ǥ ˆ–‡” „—›‹‰ —•‹…ǡ •Š‡ Šƒ† x x x 3 2 4 3 12 6 2 c m , which the stem states is equal to $60: & $ $ x x 2 60 120 ǡ ƒ•™‡”…Š‘‹…‡ ȋ ȌǤ ‡•–‹‰ –Š‡…Š‘‹…‡• ƒ› „‡ ƒ ˆƒ•–‡” ƒ’’”‘ƒ…ŠǤ ˆ–‡” „—›‹‰ „‘‘•ǡ ›† had three-fourths of the original amount left, and after buying music, •Š‡ Šƒ† –™‘Ǧ–Š‹”†• ‘ˆ ™Šƒ– ”‡ƒ‹‡† Ž‡ˆ–Ǥ –ƒ”– ™‹–Š ȋ Ȍǣ –Š”‡‡Ǧˆ‘—”–Š• ‘ˆ ̈́ͺͲ ‹• ̈́͸Ͳǡ ƒ† –™‘Ǧ–Š‹”†• ‘ˆ ̈́͸Ͳ ‹• ̈́ͶͲǡ ™Š‹…Š ‹• Ž‡•• –Šƒ –Š‡ ̈́͸Ͳ •–ƒ–‡† ‹ –Š‡ •–‡Ǥ Š‡ ‰‹ˆ– —•– Šƒ˜‡ „‡‡ Žƒ”‰‡” –Šƒ ̈́ͺͲǤ ‡•– ȋ Ȍǣ –Š”‡‡Ǧˆ‘—”–Š• ‘ˆ ̈́ͳͲͲ ‹• ̈́͹ͷǡ ƒ† –™‘Ǧ–Š‹”†• ‘ˆ ̈́͹ͷ ‹• ̈́ͷͲǡ ™Š‹…Š ‹• •–‹ŽŽ Ž‡•• –Šƒ ̈́͸ͲǤ Š‡ ƒ•™‡” —•– „‡ ȋ ȌǤ