lsv Posted January 8, 2007 Share Posted January 8, 2007 1/ Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy? (1) She bought $4.40 worth of stamps. (2) She bought an equal number of $0.15 stamps and $0.29 stamps. 2/ The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 72 black cars in the lot, how many red cars are there in the lot? 11 15 24 27 32 3/ If the average (arithmetic mean) of x, y, and 20 is 10 greater than the average of x, y, 20, and 30, what is the average of x and y? 4/ In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l? (1) The product of the slopes of line l and line k is –1. (2) Line k passes through the origin. Quote Link to comment Share on other sites More sharing options...
Fabrisco Posted January 8, 2007 Share Posted January 8, 2007 Question 1: The problem can be expressed in an equation as following: 0.15 X + 0.29 Y = Z, where X and Y are the prices of the stamps, and Z the total amount of the purchase. (1) says that Z = $4.40 It doesn't allow to solve the equation by itself --> INSUFF (2) says that X=Y so we can replace Y by X. We still have two unknown variables (X and Z) --> INSUFF (1) and (2) : replacing all variables by the given information, only X remains --> SUFFICIENT Quote Link to comment Share on other sites More sharing options...
shamit1982 Posted January 8, 2007 Share Posted January 8, 2007 1) A If .15x + .29y = 4.40. The only combination I got to work was y=10 and x=10. Since we are working with a 9 in the hundreths digit, and the total sum has a 0, y has to be a multiple of 5. It can only be 0, 5, 10, 15. Anything else would be over 4.40. The only one that can work is 10. Forcing x=10. 2) D R/B = 3/8 R = (3/8)B --> R = (3/8)*72 = 27 3) 115 x+y+20 / 3 = x+y+20+30/4 + 10 -> solve for x+y = 230 x+y / 2 = 115 4) C Each individual statement was insuff, but together you can figure out slope of k = 3/4. Then solve for (3/4)*I = -1. I = -4/3. Quote Link to comment Share on other sites More sharing options...
lsv Posted January 9, 2007 Author Share Posted January 9, 2007 1) A If .15x + .29y = 4.40. The only combination I got to work was y=10 and x=10. Since we are working with a 9 in the hundreths digit, and the total sum has a 0, y has to be a multiple of 5. It can only be 0, 5, 10, 15. Anything else would be over 4.40. The only one that can work is 10. Forcing x=10. 3) 115 x+y+20 / 3 = x+y+20+30/4 + 10 -> solve for x+y = 230 x+y / 2 = 115 4) C Each individual statement was insuff, but together you can figure out slope of k = 3/4. Then solve for (3/4)*I = -1. I = -4/3. Qn 1/ Other than random trial and error, can anyone propose a diff method ? Thanks.. I'd like to know if there are any alternative ways to solve.. Qn 3/ 95 - I'd think. Qn 4/ Stmt 1) m1*m2 =-1 Insuff Stmt 2) Let us write the equation of like k: y=mx+c => 12/5 = (16/5)m+c. The line passes through the origin. So, c = 0. m = 3/4. So, only B should be enough, isnt it ?? Pl clarify.. Thanks.. Quote Link to comment Share on other sites More sharing options...
Cippo Posted January 9, 2007 Share Posted January 9, 2007 q1: I think is D. in both case a try and error technic should work as an explanation. Reasoning about number of variable and number of equation, I agree with Fabrisco however in both cases (1 and 2) there are only one combination possible. Quote Link to comment Share on other sites More sharing options...
shamit1982 Posted January 9, 2007 Share Posted January 9, 2007 Qn 1/ Other than random trial and error, can anyone propose a diff method ? Thanks.. I'd like to know if there are any alternative ways to solve.. Qn 3/ 95 - I'd think. Qn 4/ Stmt 1) m1*m2 =-1 Insuff Stmt 2) Let us write the equation of like k: y=mx+c => 12/5 = (16/5)m+c. The line passes through the origin. So, c = 0. m = 3/4. So, only B should be enough, isnt it ?? Pl clarify.. Thanks.. Qn 1: I agree with cippo that you can solve for how many stamps using B with trial and error. Qn3: Math error on my part lsv is correct. a+b = 190....so avg = 95 Qn4: The question asks for the slope of I, not just the slope of k. I think you need both a and b to solve this. Quote Link to comment Share on other sites More sharing options...
Okukuseku Posted January 10, 2007 Share Posted January 10, 2007 1. Try and error seems the only approach but the question is how do you know instantly that a (10,10) choise will work. Any Mathematic approach? Or else most guys (including myself) would have settled with a C. 2. R/B = 3/8 , so if B = 72 => R is (72/8)*3 which is 27 3. yeah a 95 ie (190/2) 4. It should be a C not B because we need the slope of L not K. Quote Link to comment Share on other sites More sharing options...
andes Posted January 10, 2007 Share Posted January 10, 2007 Qn 1: I agree with cippo that you can solve for how many stamps using B with trial and error. Qn3: Math error on my part lsv is correct. a+b = 190....so avg = 95 Qn4: The question asks for the slope of I, not just the slope of k. I think you need both a and b to solve this. u guys be careful. when u say u can solve with information provided in statement B using trial and error, I think you are bringing information from A. Ignore statement A and look at the problem ------------------------------------------------------------------ Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy She bought an equal number of $0.15 stamps and $0.29 stamps ------------------------------------------------------------------ what trial and error you are talking about???? from statement A .15x+.29y=4.40 the above equation is in the form of ax+by = (a+b)*m ".15x+.29y=(.15+.29)*10" so as a rule, if a constant in a linear equation is a mutiple of sum of the coefficients of x & y, then x and y have to be equal. So the answer is A Quote Link to comment Share on other sites More sharing options...
Cippo Posted January 10, 2007 Share Posted January 10, 2007 I'm sorry andes you are right the answer is A Quote Link to comment Share on other sites More sharing options...
r1234 Posted January 10, 2007 Share Posted January 10, 2007 Q1: Hi cippo, andes, Though arrived at answer A, based on trial and error approach, the second option (B) clearly says the stamps bought were equal in number. so, how could you ignore B as if that was not given. If statement (B) reads something else, then I will say the answer is A, but for this question the answer should be C. ISV, could you post the OA? Quote Link to comment Share on other sites More sharing options...
lsv Posted January 11, 2007 Author Share Posted January 11, 2007 Q1: Hi cippo, andes, Though arrived at answer A, based on trial and error approach, the second option (B) clearly says the stamps bought were equal in number. so, how could you ignore B as if that was not given. If statement (B) reads something else, then I will say the answer is A, but for this question the answer should be C. ISV, could you post the OA? It is A. Can someone clarify qn 4 ? Quote Link to comment Share on other sites More sharing options...
andes Posted January 11, 2007 Share Posted January 11, 2007 Qn 1/ Other than random trial and error, can anyone propose a diff method ? Thanks.. I'd like to know if there are any alternative ways to solve.. Qn 3/ 95 - I'd think. Qn 4/ Stmt 1) m1*m2 =-1 Insuff Stmt 2) Let us write the equation of like k: y=mx+c => 12/5 = (16/5)m+c. The line passes through the origin. So, c = 0. m = 3/4. So, only B should be enough, isnt it ? Pl clarify.. Thanks.. with statement B you got the slope of k, but the question asks for the slope of l Quote Link to comment Share on other sites More sharing options...
MikeJung Posted January 23, 2007 Share Posted January 23, 2007 A D 115 C for me Quote Link to comment Share on other sites More sharing options...
donselma Posted January 23, 2007 Share Posted January 23, 2007 On question 2, isn't it saying there are 8 black cars for every three red cars, not three red cars out of eight total cars, so the ratio should be 3/11, not 3/8 (because that's saying there's only 5 black cars for every three red cars) . . . but then the problem isn't solvable. Quote Link to comment Share on other sites More sharing options...
donselma Posted January 23, 2007 Share Posted January 23, 2007 never mind, 72 blacks cars, not total cars . . . my bad . . . Quote Link to comment Share on other sites More sharing options...
donselma Posted January 23, 2007 Share Posted January 23, 2007 nice catch there, shamit on three . . . = ) Quote Link to comment Share on other sites More sharing options...
asdada1 Posted January 23, 2007 Share Posted January 23, 2007 1) A If .15x + .29y = 4.40. The only combination I got to work was y=10 and x=10. Since we are working with a 9 in the hundreths digit, and the total sum has a 0, y has to be a multiple of 5. It can only be 0, 5, 10, 15. Anything else would be over 4.40. The only one that can work is 10. Forcing x=10. 2) D R/B = 3/8 R = (3/8)B --> R = (3/8)*72 = 27 3) 115 x+y+20 / 3 = x+y+20+30/4 + 10 -> solve for x+y = 230 x+y / 2 = 115 4) C Each individual statement was insuff, but together you can figure out slope of k = 3/4. Then solve for (3/4)*I = -1. I = -4/3. agree but I get sol for 3 as 95 Quote Link to comment Share on other sites More sharing options...
asdada1 Posted January 23, 2007 Share Posted January 23, 2007 It is A. Can someone clarify qn 4 ? eqn of line = y=mx+c A) with eqn we know prod of slopes is -1 but we have neither slopes hence not suff b) says one line passes through origin (0,0) subs in y=mx+c we get c=0 but no m so in suff when we take both and since we know other point is (12/5,16/5) we can derive the new eqn which is y=mx+C but c is 0 hence y=mx subs values 12/5=m(16/5) m=3/4 we know the prod of the 2 slopes in -1 hence the other slope must be -4/3 Hence C HTH Quote Link to comment Share on other sites More sharing options...
bose Posted May 4, 2008 Share Posted May 4, 2008 for q4 its C Quote Link to comment Share on other sites More sharing options...
shyamprasadrao Posted September 14, 2008 Share Posted September 14, 2008 why should i consider trial and error to answer a DS ques... i thought the statement by itself was sufficient.. please advice Quote Link to comment Share on other sites More sharing options...
megha57 Posted September 15, 2008 Share Posted September 15, 2008 IMO: 1. The answer will be C. With both the statements it becomes a matter of solving an equation, which we can do. Many people are talking about trial and error. Lets consider just the statement 1. it says; 0.15*x + 0.29*y = 4.4 x is number of $0.15 stamps and y is number of $0.29stamps. Well there can be n number of solutions for this. How do we know when to stop. I dont think DS is suppose to be solved like that. Hence answer should be C 2. answer is 27. Red/Black = 3/8 hence red = 27 (when black is 72) 3. Answer is 95 Solve the equation for x+y: (x+y+20)/3 = (x+y+20+30)/4 + 10 x+y = 190 Hence average = 95 4. Answer should be C. Just by knowing product of slopes and the intersection point we can not determine any information. Just by knowing K passes through origin, we can only determine equation for k but nothing about line l. But if we put that together. From two we can get equation & slope for line k. As product of slopes is given by statement 1 we can fine slope for l. Quote Link to comment Share on other sites More sharing options...
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