GMAT Word Problems: Fundamentals (Excerpt)

Transcription

1 GMAT Word Problems: Fundmentls (Excerpt) Jeff Sckmnn / GMAT HACKS Jnury 2013 Contents 1 Introduction 2 2 Difficulty Levels 3 3 Problem Solving 4 4 Dt Sufficiency 6 5 Answer Key 8 6 Explntions 9 1

2 1 Introduction This document contins nothing but GMAT Word Problems questions 100 of them, to be exct. There s nothing inherently difficult bout word problem, but very few GMAT word problems re very esy. The biggest chllenge most students fce is trnslting the word problem to n lgebr problem (or whtever content re it is). The mth my not be hrd, but getting to the point where you cn do the mth tkes prctice. As in ll of my GMAT preprtion resources, you ll find these questions indexed by difficulty. For further, more specific prctice, I hve produced severl other resources tht my help you. There re mny word problems in nerly ll of my prctice sets, but you ll find the most in Rtes, Rtios, nd Percents, nd Problem Solving: Fundmentls. There re lso mny tricky ones in Algebr: Fundmentls, in prticulr severl tht hve vribles in the nswer choices. Also, Totl GMAT Mth hs severl chpters (long with focused prctice) on just bout every type of word problem, including individul chpters on rtios, rtes, verges, weighted verges, overlpping sets, probbility, permuttions, combintions, nd much more. If you find you re struggling with the mechnics of these problems, your time is probbly better spent with Totl GMAT Mth thn in doing dozens nd dozens of prctice problems, hoping to pick up those skills long the wy. As fr s strtegy is concerned, there re dozens of rticles t gmthcks.com to help you with your strtegic pproch to Arithmetic questions. Most importntly, you should mke sure you understnd every prctice problem you do. It doesn t mtter if you get it right the first time wht mtters is whether you ll get it right the next time you see it, becuse the next time you see it could be on the GMAT. With tht in mind, crefully nlyze the explntions. Redo questions tht took you too long the first time round. Review questions over multiple sessions, rther thn crmming for eight hours stright ech Sturdy. These bsic study skills my not feel like the key to GMAT preprtion, but they re the difference between those people who rech their score gols nd those who never do. Enough tlking; there re 100 Word Problems questions witing inside. Get to work! 2

3 2 Difficulty Levels In generl, the level 5 questions in this guide re 500- to 560-level questions. The level 4 questions represent brod rnge of difficulty from bout 380 to 500, while the level 3 questions re lower. Esy (3) PS 9, 12, 30 DS 47, 50, 55, 59, 63, 74, 76, 82, 84, 96 Modertely Esy (4) PS 3, 4, 7, 8, 11, 18, 22, 23, 27, 28, 32, 33, 34, 36, 38, 40, 42, 43 DS 46, 48, 49, 53, 54, 56, 57, 58, 60, 61, 62, 64, 65, 66, 75, 77, 78, 79, 83, 85, 91, 92, 94, 95, 97, 98, 99, 100 Moderte (5) PS 1, 2, 5, 6, 10, 13, 14, 15, 16, 17, 19, 20, 21, 24, 25, 26, 29, 31, 35, 37, 39, 41, 44, 45 DS 51, 52, 67, 68, 69, 70, 71, 72, 73, 80, 81, 86, 87, 88, 89, 90, 93 3

4 3 Problem Solving Note: this guide contins both n nswer key (so you cn quickly check your nswers) nd full explntions. 41. Country X txes ech of its citizens n mount equl to 12 percent of the first $40,000 of income, plus 20 percent of ll income in excess of $40,000. If citizen of Country X is txed totl of $8,000, wht is her income? (A) $40,000 (B) $56,000 (C) $64,000 (D) $66,667 (E) $80, The mnger of concert venue noted tht for every 100 dmission tickets sold, the venue sells 12 compct discs t $15.00 ech, 8 t-shirts t $20.00 ech, nd 5 concert posters t $12.00 ech. Wht is the verge (rithmetic men) of these merchndise sles per ticket sold? (A) $3.00 (B) $3.76 (C) $3.81 (D) $4.00 (E) $4.40 $10, $11, $11, $12, $12, $14, $16, $17, $21, $ The vrious prices tht certin product were sold for t retilers in City X is shown bove. How mny prices were greter thn the medin price but less thn the men price? (A) (B) (C) (D) (E) None One Two Three Four 4

5 44. Tr drove t n verge speed of 50 miles per hour for the first 50 miles of her trip nd then t n verge speed of 75 miles per hour for the remining 50 miles of her trip. If she mde no stops during the trip, wht ws Tr s verge speed, in miles per hour, for the entire trip? (A) 50 (B) 55 (C) 60 (D) 65 (E) Running t the sme constnt rte, identicl mchines cn produce totl of 120 bolts per minute. At this rte, how mny bolts could 4 such mchines produce in 5 minutes? (A) (B) (C) 150 (D) 480 (E) 2,400 5

6 4 Dt Sufficiency For ll Dt Sufficiency questions, the nswer choices re s follows: (A) (B) (C) (D) (E) Sttement (1) ALONE is sufficient, but sttement (2) lone is not sufficient. Sttement (2) ALONE is sufficient, but sttement (1) lone is not sufficient. BOTH sttements TOGETHER re sufficient, but NEITHER sttement ALONE is sufficient. EACH sttement ALONE is sufficient. Sttements (1) nd (2) TOGETHER re NOT sufficient. 46. If x eqully priced shres of certin stock were vlued t $25,000 on Mondy, wht ws the vlue per shre of the stock on Fridy? (1) The vlue of ech shre incresed by 3% between Mondy nd Fridy. (2) The vlue of ech shre incresed by $1.50 between Mondy nd Fridy. 47. Steve nd Crl ech received n increse in slry. Which one received the lrger percent increse? (1) Steve s slry incresed by $1,000 per month. (2) Crl s slry incresed by $1,200 per month 48. A sporting goods store tht sells tennis blls sells ech of its pckges of Brnd X blls for certin price nd ech of its pckges of Brnd Y blls for certin price. If Oscr, Rennie, nd Thom bought tennis blls in this store, how much did Rennie py for 2 pckges of Brnd X blls nd 2 pckges of Brnd Y blls? (1) Oscr bought 2 pckges of Brnd X blls nd 1 pckge of Brnd Y blls for $9.49. (2) Thom bought 1 pckge of Brnd X blls nd 1 pckge of Brnd Y blls for $ If n item is purchsed for x percent less thn its retil price, nd then sold for y percent less thn its retil price, wht ws the retil price of the item? (1) x y = 10 (2) y = 5 6

7 50. Bord member A wnts to schedule 30-minute meeting on Tuesdy with himself nd three other bord members, B, C, nd D. Is there 30-minute period on Tuesdy tht is open for ll four members? (1) On Tuesdy A nd C hve n open period from 9:30.m to 11:00.m. (2) On Tuesdy D hs n open period from 10:30.m. to 1:00 p.m. nd B hs n open period from 8:00.m. to 12:00 p.m. 7

8 5 Answer Key For full explntions, see the next section. 41. B 42. D 43. B 44. C 45. E 46. C 47. E 48. B 49. E 50. C 8

9 6 Explntions For quick-reference nswer key, see the previous section. 41. B Explntion: 12 percent of the first $40,000 in income is: 0.12(40, 000) = 12(400) = 4800 Tht s less thn $8,000, so the citizen s income must be more thn $40,000. If the citizen ws txed $4,800 on the first $40,000 in income, tht leves $8, 000 $4, 800 = $3, 200 in tx on the remining income. The tx rte on dditionl income is 20%. If we cll the dditionl income, we cn set 20% of equl to $3,200: 3200 = 0.2 = 3200(5) = 16, 000 If the citizen erns $16,000 fter the first $40,000, tht s totl of $56,000, choice (B). 42. D Explntion: First, find the totl merchndise sles per 100 dmission tickets: 12 compct discs t $15 ech is: 12(15) = $180 8 t-shirts t $20 ech is: 8(20) = $160 5 posters t $12 ech is 5(12) = $60 The totl is $180 + $160 + $60 = $400 $400 per 100 is $4 per ticket, choice (D). 43. B Explntion: To find the medin, first rrnge the terms in scending order. (Tht s lredy done for you.) Since there re n even number of terms in the set, the medin is the verge of the two middle terms, $12 nd $14, for medin of $13. To find the men price, divide the sum of the prices by the number of prices (10): = = 14.6 To nswer the question: how mny terms re greter thn the medin price of $13 nd less thn the men price of $14.60? The only term tht fits tht description is $14, so the nswer is one, choice (B). 44. C Explntion: To find verge speed, find the totl distnce nd the totl time. Totl distnce is strightforwrd: there re two 50-mile segments, for totl of 100 miles. Totl time requires more effort. If she drove t speed of 50 miles per hour for the first 50 miles, tht s time of 1 hour. 9

10 The next segment is 75 miles per hour for 50 miles: tht requires some lgebr: t = d r = = 2 3 Totl time for the entire trip is 1 hour plus 2 3 of n hour. Averge speed is totl distnce divided by totl time: s = 100 = = 100( 3 5 ) = 60, choice (C) E Explntion: This is bit chllenging to get hndle on, so try choosing vlue for. If = 10 mchines, then 10 identicl mchines cn produce totl of 120 bolts per minute. Tht 12 bolts per minute per mchine. In other words, we cn find the rte per minute per mchine by dividing 120 by : lgebriclly, tht s 120 bolts per minute per mchine. If you hve four mchines, you cn multiply tht rte per minute per mchine by 4: 120 (4) bolts per minute for four mchines. If the mchines will work for 5 minutes, multiply tht rte per minute by 5: 120 (4)(5) bolts for four mchines in five minutes. Simplified, tht is: 120(4)(5), choice (E). = 2, C Explntion: Sttement (1) is insufficient: we cn determine from this the totl vlue of the shres on Fridy, but tht doesn t help us find the vlue of ech individul shre. Sttement (2) is lso insufficient: this gives us some informtion bout individul shres, but since we don t know the vlue per shre on Mondy, we cn t determine the vlue per shre on Fridy. Tken together, the sttements re sufficient. If the totl vlue incresed by 3% from Mondy to Fridy, the vlue per shre did s well. If tht increse is equl to $1.50, we cn find the originl price: 0.03x = 1.50 where x is the Mondy price per shre. Find tht, dd $1.50, nd you hve the Fridy price per shre. Choice (C) is correct. 47. E Explntion: Sttements (1) nd (2) re insufficient for the sme reson: without knowing ech person s originl slry, we don t know wht percent increse those dollr mounts represent. Tken together, the sttements re still insufficient. While Crl received the lrger dollr mount increse, it s possible tht Steve received the lrger percent increse. If Crl s strting slry ws much lrger, $1,200 per month increse my not be s lrge of percent increse s $1,000 per month increse on smller strting slry. Choice (E) is correct. 48. B 10

11 Explntion: Sttement (1) is insufficient: it llows us to set up n eqution with two vribles, but tht s not enough to solve for ech vrible: 2x + y = 9.49 Sttement (2) is sufficient. Agin, we get n eqution with two vribles, but this time we cn trnslte it into the nswer to the question: x + y = 6.49 Multiply both sides by 2 to get the price of 2 pckges of Brnd X blls nd 2 pckges of Brnd Y blls: 2x + 2y = 2(6.49) Choice (B) is correct. 49. E Explntion: Mny dt sufficiency questions require tht you hve n ctul number, whether it be price, popultion size, or the length of geometric figure. This is one of them: x nd y represent percents, but in order to know the retil price, you ll need to know some number such s $30 or $100. It only tkes quick glnce t the sttements to relize tht (E) must be the correct choice, s the sttements re concerned with the percents, not the price. Without price, you cn t nswer the question. 50. C Explntion: Sttement (1) is insufficient: it gives us no informtion bout B or D. Sttement (2) is lso insufficient: there is n overlp between B s free time nd D s free time, but we don t know whether tht time period overlps with vilbility from A nd C. Tken together, the sttements re sufficient. (2) tells us tht B nd D re both vilble from 10:30.m. to 12:00 p.m., nd (1) tells us tht A nd C re vilble from 10:30.m. to 11:00.m. They cn meet for tht 30-minute period. Choice (C) is correct. 11