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# URGENT help required, OG 13 questions

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Manager
Joined: 30 Mar 2013
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URGENT help required, OG 13 questions [#permalink]

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08 Apr 2013, 08:57
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Q1)A ladder of a fire truck is elevated to an angle of 60 degrees and extended to a length of 70 feet. if the base of the ladder is 7 fet above the ground, how many feet above the ground does the ladder reach?
a) 35
b) 42
c) 35 \sqrt{3}
d) 7+ 35\sqrt{3}
e) 7+42\sqrt{3}

Q2) the price of lunch for 15 people was $207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity? a)11.73 b)12 c)13.8 d)14 e)15.87 Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301? a) 10,100 b) 20,200 c) 22,650 d) 40,000 e) 45,150 Q4)Last year the price per share of stock X increased by k percent and the earnings per share of stock X increased by m percent, where k is greater than m. By what percent is the ratio of price per share to the earnings per share increase, in terms of k and m? a) k/m b) k-m c) [100(k-m)]/ 100+k d) [100(k-m)]/[100+m] e) [100(k-m)/(100+k+m) Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects? a)105 b)125 c)130 d)180 e)195 Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x? a)100m b)1/(100m) c) 1/m d) 10/m e) 10,000/m Q7) Seven pieces if rope have an average of length of 68 cmand median length of 84 cm. if the length f the longest piece of rope is 14 cm more than 4 times the length of the shortest piece of rope, what si maximum possible length , in cm, of the longest piece of rope? a)82 b)118 c)120 d)134 e)152 Q8) [0.99999999/1.0001]- [0.99999991/1.0003]= a) 10^-8 b) 3(10^-8) c) 3 (10^-4) d) 2(10^-4) e) 10^-4 Q9) List T consists of 30 positive decimals, none of which is an integer, and the sum of 30 decimals is S. the estimated sum of the 30 decimals, E is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E-S? 1. -16 2. 6 3.10 A) 1 only B) 1 and 2 only C) 1 and 3 only D) 2 and 3 only E) 1,2 and 3 Last edited by bb on 13 Apr 2013, 00:18, edited 2 times in total. Edited the question. VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1123 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Followers: 184 Kudos [?]: 1998 [2] , given: 219 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:05 2 This post received KUDOS That's a lot of questions ! Q1)A ladder of a fire truck is elevated to an angle of 60 degrees and extended to a length of 70 feet. if the base of the ladder is 7 fet above the ground, how many feet above the ground does the ladder reach? The ladder forms a 30 60 90, triangle which has dimentions 1x $$\sqrt{3}$$ 2, the hip is $$70=2x$$ so $$x=35$$, the H of the triangle is $$35\sqrt{3}$$, but the ladder is 7 feet from the ground => it reaches $$7+35\sqrt{2}$$ IMO D _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1123 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Followers: 184 Kudos [?]: 1998 [2] , given: 219 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:08 2 This post received KUDOS Q2) the price of lunch for 15 people was$207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity?

X=price
$$x+0.15x=207, 1.15x=207, x=\frac{207}{1.15}, x=180$$
They paid 180 $tot, so $$\frac{180}{15}=12$$ each IMO B _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1123 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Followers: 184 Kudos [?]: 1998 [3] , given: 219 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:14 3 This post received KUDOS Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301? 100 ... 200 ... 300 Between 200 and 100 there are 200/2-100/2+1=51 even integers Between 300 and 200 there are 300/2-200/2+1=51 even integers But we counted 200 twice, so tot even entegers = $$51+51-1=101.$$ As you can see their mean is 200 So tot sum is$$200*101=20200$$ IMO B _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] Manager Status: Looking to improve Joined: 15 Jan 2013 Posts: 177 GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31 Followers: 1 Kudos [?]: 64 [1] , given: 65 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:18 1 This post received KUDOS Quote: Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301? a) 10,100 b) 20,200 c) 22,650 d) 40,000 e) 45,150 Sum of all even integers is Avg. * count of numbers in series 99 - 301 Avg = first + last / 2 = 100 + 300 / 2 = 200 count of numbers in the series = 300 - 100 / 2 + 1 = 101 Sum = 200 * 101 = 20200. Answer is B //Kudos please, if the above explanation is good _________________ KUDOS is a way to say Thank You Manager Status: Looking to improve Joined: 15 Jan 2013 Posts: 177 GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31 Followers: 1 Kudos [?]: 64 [1] , given: 65 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:22 1 This post received KUDOS Quote: Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x? a)100m b)1/(100m) c) 1/m d) 10/m e) 10,000/m x = (m/100)*y y/x = (y/m*y/100)*100 = 10,000/m . Answer is E //kudos please, if the above explanation is good _________________ KUDOS is a way to say Thank You VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1123 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Followers: 184 Kudos [?]: 1998 [2] , given: 219 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:24 2 This post received KUDOS 1 This post was BOOKMARKED Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects? Use the formula : Tot = S+V+D-(two)+2(three) = 100 300 = 120 + 90 + 225 - 105 - 2*(three) so 15 had all three To see the number of subjects with 1 effect: S+V+D-2*two-3*three = 435 - 210 - 45 = 180 Refer to this formulae-for-3-overlapping-sets-69014.html _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1123 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Followers: 184 Kudos [?]: 1998 [1] , given: 219 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:28 1 This post received KUDOS Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x? $$x= \frac{m}{100}y$$ $$100x=m*y$$ $$y= \frac{100}{m}x$$ $$y= (10000/m)/100 (of) x$$ $$y = \frac{10,000}{m}$$ IMO E _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 630 Followers: 82 Kudos [?]: 1137 [1] , given: 136 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:41 1 This post received KUDOS Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x? a)100m b)1/(100m) c) 1/m d) 10/m e) 10,000/m Assume m=100%. Thus x=y, only E gives the answer as 100%. E. _________________ Intern Joined: 06 Apr 2012 Posts: 38 Location: France Concentration: Finance, Entrepreneurship GPA: 3.4 Followers: 0 Kudos [?]: 7 [1] , given: 7 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:42 1 This post received KUDOS Free OG video explanations here: http://www.gmatquantum.com/og13th/ Thanks to gmatclub member dabral Manager Joined: 11 Jun 2010 Posts: 84 Followers: 0 Kudos [?]: 18 [1] , given: 17 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:45 1 This post received KUDOS Q.6 x = my/100 we have to find 100y/x = ? y/x = 100/m Multiple both sides by 100 100y/x = 10000 / m hence E is the answer Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 630 Followers: 82 Kudos [?]: 1137 [1] , given: 136 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:45 1 This post received KUDOS Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301? a) 10,100 b) 20,200 c) 22,650 d) 40,000 e) 45,150 No of even terms between 99 and 301-->(300-100)/2 +1 = 101. Thus the sum = $$101/2 * (100+300)$$ = 200*101 = 20200 B. _________________ Manager Status: Looking to improve Joined: 15 Jan 2013 Posts: 177 GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31 Followers: 1 Kudos [?]: 64 [2] , given: 65 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 09:47 2 This post received KUDOS Quote: Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects? Let x represent subjects who experienced only sweaty palms Let y represent subjects who experienced only vomiting Let z represent subjects who experienced only dizziness Let a represent subjects who experienced only sweaty palms and dizziness Let b represent subjects who experienced only sweaty palms and vomiting Let c represent subjects who experienced only vomiting and dizziness Let d represent subjects who experienced vomiting, sweaty palms, and dizziness x+a+b + d = 120 y+b+c +d = 90 z+a+c +d = 225 x+y+z +2 (a+b+c) - 3d = 120 + 90 + 225 - 105 - 3*15 = 180 Answer : D //kudos please, if the above explanation is good _________________ KUDOS is a way to say Thank You Manager Joined: 11 Jun 2010 Posts: 84 Followers: 0 Kudos [?]: 18 [1] , given: 17 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 10:05 1 This post received KUDOS Q7. Mean of 7 wood pieces = 68 therefore total length of 7 pieces = 68 * 7 = 476 cms Median of 7 pieces = 84 To have the 7th piece of maximum length we must have 4th, 5th, 6th piece = median length of 84 and 1st, 2nd and 3rd piece = smallest wood length. 1st (SMALLEST) --- 2nd (SMALLEST) --- 3rd (SMALLEST) --- 4th (MEDIAN) --- 5th (MEDIAN) --- 6th (MEDIAN) --- 7th (LONGEST) Sum (4th, 5th and 6th) = 84 * 3 = 252 cms Let smallest wood piece be x cms Sum (1st, 2nd and 3rd) = 3x Longest piece = 4*smallest + 14 therefore 252 + 3x + 4x + 14 = 476 x = 30 hence longest piece = 134 cms Ans D Manager Joined: 11 Jun 2010 Posts: 84 Followers: 0 Kudos [?]: 18 [1] , given: 17 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 10:12 1 This post received KUDOS Q8. lets remove decimals first from both the denominators 9999 / 10001 - 9999 / 10003 => {(10003 - 10001) * 9999} / 10^8 => 2 * 9999 / 10^4 since 9999 is approx 10000 or 10^4 we can wrire 2 * 10^4 / 10^8 or 2 * 10^(-4) hence D is answer Manager Joined: 11 Jun 2010 Posts: 84 Followers: 0 Kudos [?]: 18 [1] , given: 17 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 10:15 1 This post received KUDOS Q5. 100 = 40 + 30 + 75 - 35 - 2(all three) All three = 5% therefore 2 effects + 3 effects = 40% hence % who only experienced one fo the effects = 60% 60% of 300 = 180 students hence D Manager Status: Looking to improve Joined: 15 Jan 2013 Posts: 177 GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31 Followers: 1 Kudos [?]: 64 [1] , given: 65 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 10:19 1 This post received KUDOS Q9) Let the 30 decimals be d1, d2, d3,... d30 and corresponding 30 integers are i1, i2, i3,... i30 The integer set will have 1/3 of the numbers will be higher by 1 from decimal set and 2/3 of the numbers will be lower by 1 from decimal set. E - S = 1/3S - 2/3S - S = -4/3S. Looking at the options only -16 can be an integer result of -4/3S Hence the answer is A - I only //kudos please, if the above explanation is good. _________________ KUDOS is a way to say Thank You Last edited by nt2010 on 08 Apr 2013, 10:21, edited 1 time in total. Manager Joined: 11 Jun 2010 Posts: 84 Followers: 0 Kudos [?]: 18 [1] , given: 17 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 10:20 1 This post received KUDOS Q2. 1.15x = 207 x = 180 cost of 15 people = 180 (without gratuity) cost per person = 180 / 15 = 12 hence B Manager Joined: 11 Jun 2010 Posts: 84 Followers: 0 Kudos [?]: 18 [0], given: 17 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 10:23 Q3. sum of evenly spaced sets = avg of 1st and last term * # of terms Avg of first and last = avg (100,300) = 200 # of terms = {(300 - 100)/ 2} + 1 = 101 terms hence sum = 200 * 101 = 20200 Ans B Intern Joined: 08 Mar 2013 Posts: 3 Followers: 0 Kudos [?]: 2 [1] , given: 1 Re: URGENT help required, OG 13 questions [#permalink] ### Show Tags 08 Apr 2013, 10:29 1 This post received KUDOS Q2) the price of lunch for 15 people was$207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity?
a)11.73
b)12
c)13.8
d)14
e)15.87

Here the word EXCLUDING is used.
So 0.15 * 207=$31.05 Therefore,207-31.05=$175.95

So the average cost per person=175.75/15=11.73
So ans should be (A) IMO.
Re: URGENT help required, OG 13 questions   [#permalink] 08 Apr 2013, 10:29

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