Victory for the ACT Student Text 15e

M ATH Q UIZZES • 259

EXPLANATIONS

2. ‘”ƒŽ †‘œ‡…‘–ƒ‹• ͳʹ ‹–‡•ǡ ƒ† ƒ „ƒ‡”ǯ• †‘œ‡…‘–ƒ‹• ͳ͵ ‹–‡•Ǥ ˆ x is the number of items that could be measured either in a whole number of normal †‘œ‡• ‘” ‹ ƒ ™Š‘Ž‡ —„‡” ‘ˆ „ƒ‡”ǯ• dozens, what is the minimum value of x ? F. 1 G. 12 H. 13 J. 25 K. 156  –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ ™Šƒ– ‹• –Š‡ †‡‰”‡‡ measure of the smaller ‘ˆ –Š‡ –™‘ ƒ‰Ž‡• ˆ‘”‡† „› –Š‡ Š‘—” ƒ† ‹—–‡ Šƒ†• ‘ˆ –Š‡…Ž‘…ǫ Ǥ 45 B. 60 C. 90 D. 120 E. 240 4. –ƒ”–‹‰ ˆ”‘ ’‘‹–• –Šƒ– ƒ”‡ ʹͲͲ ‹Ž‘‡–‡”• ƒ’ƒ”–ǡ –™‘ –”ƒ‹• –”ƒ˜‡Ž –‘™ƒ”† ‡ƒ…Š ‘–Š‡” ƒŽ‘‰ –™‘ ’ƒ”ƒŽŽ‡Ž –”ƒ…•Ǥ ˆ ‘‡ –”ƒ‹ –”ƒ˜‡Ž• ƒ– ͹Ͳ ‹Ž‘‡–‡”• ’‡” Š‘—” ƒ† –Š‡ ‘–Š‡” –”ƒ˜‡Ž• ƒ– ͺͲ ‹Ž‘‡–‡”• ’‡” hour, how much time, in hours, will elapse before the trains pass each other? F. 4 3 G. 1 H. 3 4 J. 2 3 K. 2 3.

2. (K) Mathematics/Number and Quantity/ Basic Arithmetic Manipulations Š‡ ƒ•™‡” ‹• –Š‡ ϐ‹”•– —„‡” –Šƒ– ‹• †‹˜‹•‹„Ž‡ „› „‘–Š ͳʹ ƒ† ͳ͵ǣ ͳͷ͸ ( 156 12 13 : ).

3. (D) Mathematics/Geometry/Lines and Angles Š‡ —‡”ƒŽ• ‘ –Š‡ ˆƒ…‡ ‘ˆ –Š‡…Ž‘… divide the circumference of the circle into twelve equal 30°-arcs ( 360 12 30 ' ). Š‡”‡ˆ‘”‡ǡ –Š‡ †‡‰”‡‡ ‡ƒ•—”‡ ‘ˆ –Š‡ ƒ”… from 12 to 4 is 120. Ž–‡”ƒ–‹˜‡Ž›ǡ •‹’Ž› ‡•–‹ƒ–‡Ǥ Š‡ ƒ‰Ž‡ ‹•…Ž‡ƒ”Ž› ‰”‡ƒ–‡” –Šƒ ͻͲιǡ •‘ ‡Ž‹‹ƒ–‡ ȋ Ȍǡ ȋ Ȍǡ ƒ† ȋ ȌǤ Š‹• Ž‡ƒ˜‡• ȋ Ȍǡ ͳʹͲǡ ƒ• –Š‡ ‘Ž› ’‘••‹„Ž‡…Š‘‹…‡ǡ •‹…‡ ʹͶͲǡ ȋ Ȍǡ …‘””‡•’‘†• –‘ ƒ ƒ‰Ž‡ ‰”‡ƒ–‡” –Šƒ ƒ •–”ƒ‹‰Š– Ž‹‡Ǥ 4. (H) Mathematics/Algebra and Functions/ Solving Algebraic Equations or Inequalities with One Variable/Simple Equations Š‹• ‹–‡ ‹• •‘Ž˜‡† „› ”‡ƒŽ‹œ‹‰ –Šƒ– –Š‡ –‘–ƒŽ †‹•–ƒ…‡ –”ƒ˜‡Ž‡† „› –Š‡ –™‘ –”ƒ‹•ǡ wherever the trains meet, will equal ʹͲͲ ‹Ž‘‡–‡”•Ǥ Š—•ǡ ‹ˆ x is the time the trains travel, x x x 70 80 200 3 4 hours. hr km hr km & + = = Ž–‡”ƒ–‹˜‡Ž›ǡ Dz–‡•–Ǧ–Š‡Ǧ–‡•–ǡdz „‡‰‹‹‰ with (H): if both trains run for 3 4 hours, then the total distance traveled is 200 ‹Ž‘‡–‡”•Ǥ

The Cambridge Edge The directions ‘ –Š‡…Ž‡ƒ”Ž› •–ƒ–‡ that illustrative ‹ƒ‰‡• ƒ”‡ ‡…‡••ƒ”‹Ž› †”ƒ™ –‘ •…ƒŽ‡Ǥ —– ‹ˆ ›‘— ƒ”‡ –”—Ž› •–—… ‘ a problem with an ‹ƒ‰‡ǡ ‰‘ ƒŠ‡ƒ† and assume the ‹ƒ‰‡ ‹• †”ƒ™ –‘ •…ƒŽ‡Ǥ Š‡ ‹ƒ‰‡• are provided to ƒ••‹•– ›‘—ǡ ƒ† most of the time –Š‡› ƒ”‡ †”ƒ™ to scale or drawn ƒ……—”ƒ–‡Ž› ‡‘—‰Š •‘ –Šƒ– ›‘—…ƒ at least eliminate some answer choices.