Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49909

The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
03 Sep 2012, 06:14
Question Stats:
81% (01:33) correct 19% (01:44) wrong based on 1108 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 49909

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
03 Sep 2012, 06:14
SOLUTIONThe inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?(1) Each of the cans has a radius of 4 centimeters > radius=4 means that diameter=8, which implies that along the 48 centimeter length of the carton 48/8=6 cans can be placed and along the 32 centimeter width of the carton 32/8=4 cans can be placed. Thus, k=6*4=24. Sufficient. (2) Six of the cans fit exactly along the length of the carton > the diameter of the can is 48/6=8 centimeters. So, we have the same info as above. Sufficient. Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 15 Jun 2010
Posts: 317
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
03 Sep 2012, 06:23
Bunuel wrote: The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?
(1) Each of the cans has a radius of 4 centimeters. (2) Six of the cans fit exactly along the length of the carton.
Since Height of Box and Height of Cans are equal so only one stack of cans is there in the box. No need to bother about height. So inside dimensions of Box = 48 X 32 St 1: Sufficient: Each can has radius of 4 = Dia is 8 cms. ie (48/8) 6 nos of cans can be in one row. And since cans are identical (32/8) ie 4 cans can fit in colums. So 24 nos of can can fit in box. St 2: Sufficient: 6 cans can fit along the length. ie dia of each can = 48/6 ie 8 cms. As discussed in St 1. Hence Answer is D)
_________________
Regards SD  Press Kudos if you like my post. Debrief 610540580710(Long Journey): http://gmatclub.com/forum/from600540580710finallyachievedin4thattempt142456.html



Manager
Joined: 21 Jun 2011
Posts: 66
Location: United States
Concentration: Accounting, Finance
WE: Accounting (Accounting)

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
24 Apr 2013, 02:53
Bunuel wrote: SOLUTIONThe inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?(1) Each of the cans has a radius of 4 centimeters > radius=4 means that diameter=8, which implies that along the 48 centimeter length of the carton 48/8=6 cans can be placed and along the 32 centimeter width of the carton 32/8=4 cans can be placed. Thus, k=6*4=24. Sufficient. (2) Six of the cans fit exactly along the length of the carton > the diameter of the can is 48/6=8 centimeters. So, we have the same info as above. Sufficient. Answer: D. Kudos points given to everyone with correct solution. Let me know if I missed someone. I know the measurement of the carton, which is 48*32. Now the can's radius is 4 cm. Although the height of the carton is the same as the height of the cans i.e. 15, which I am ignoring as it will eventually cancel out in the calculation. My question is around the solution that is provided in the O.G. They have simply divided the length of the carton by diameter and width by diameter and then further multiplied the result. (48/8)*(32/8) =6*4 =24. Btw I got the right answer since its a DS problem. I am worried coz had this been a p.s problem, I might have got this one wrong. Now the way I would have solved this is 1st find the circumference of the circle (eliminating the height as the it is same). 2IIr=2*22/7*4 and then divided it by (48*32)/(176/7). My answer in this case is different from the OA =61.09 Why II (pie) was not considered. Why circumference was not considered instead of diameter. I failed to understand this. Can you please explain this. Further when I use a formula for rectangle's area =L*B, where both lenght and breadth is present. But in case of circle I don't have a II(pie) anywhere. Why do we use this. What is the significance of II (pie).



Math Expert
Joined: 02 Sep 2009
Posts: 49909

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
24 Apr 2013, 05:38
davidfrank wrote: Bunuel wrote: SOLUTIONThe inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?(1) Each of the cans has a radius of 4 centimeters > radius=4 means that diameter=8, which implies that along the 48 centimeter length of the carton 48/8=6 cans can be placed and along the 32 centimeter width of the carton 32/8=4 cans can be placed. Thus, k=6*4=24. Sufficient. (2) Six of the cans fit exactly along the length of the carton > the diameter of the can is 48/6=8 centimeters. So, we have the same info as above. Sufficient. Answer: D. Kudos points given to everyone with correct solution. Let me know if I missed someone. I know the measurement of the carton, which is 48*32. Now the can's radius is 4 cm. Although the height of the carton is the same as the height of the cans i.e. 15, which I am ignoring as it will eventually cancel out in the calculation. My question is around the solution that is provided in the O.G. They have simply divided the length of the carton by diameter and width by diameter and then further multiplied the result. (48/8)*(32/8) =6*4 =24. Btw I got the right answer since its a DS problem. I am worried coz had this been a p.s problem, I might have got this one wrong. Now the way I would have solved this is 1st find the circumference of the circle (eliminating the height as the it is same). 2IIr=2*22/7*4 and then divided it by (48*32)/(176/7). My answer in this case is different from the OA =61.09 Why II (pie) was not considered. Why circumference was not considered instead of diameter. I failed to understand this. Can you please explain this. Further when I use a formula for rectangle's area =L*B, where both lenght and breadth is present. But in case of circle I don't have a II(pie) anywhere. Why do we use this. What is the significance of II (pie). Why are you calculating the circumference?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 21 Jan 2010
Posts: 279

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
24 Apr 2013, 18:15
Straight forward question. You need to get the radius of the cylinders to get the number of cylinders. Both A and B help to calculate r. D wins.



Manager
Joined: 21 Jun 2011
Posts: 66
Location: United States
Concentration: Accounting, Finance
WE: Accounting (Accounting)

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
26 Apr 2013, 22:38
Bunuel wrote: davidfrank wrote: Bunuel wrote: SOLUTIONThe inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?(1) Each of the cans has a radius of 4 centimeters > radius=4 means that diameter=8, which implies that along the 48 centimeter length of the carton 48/8=6 cans can be placed and along the 32 centimeter width of the carton 32/8=4 cans can be placed. Thus, k=6*4=24. Sufficient. (2) Six of the cans fit exactly along the length of the carton > the diameter of the can is 48/6=8 centimeters. So, we have the same info as above. Sufficient. Answer: D. Kudos points given to everyone with correct solution. Let me know if I missed someone. I know the measurement of the carton, which is 48*32. Now the can's radius is 4 cm. Although the height of the carton is the same as the height of the cans i.e. 15, which I am ignoring as it will eventually cancel out in the calculation. My question is around the solution that is provided in the O.G. They have simply divided the length of the carton by diameter and width by diameter and then further multiplied the result. (48/8)*(32/8) =6*4 =24. Btw I got the right answer since its a DS problem. I am worried coz had this been a p.s problem, I might have got this one wrong. Now the way I would have solved this is 1st find the circumference of the circle (eliminating the height as the it is same). 2IIr=2*22/7*4 and then divided it by (48*32)/(176/7). My answer in this case is different from the OA =61.09 Why II (pie) was not considered. Why circumference was not considered instead of diameter. I failed to understand this. Can you please explain this. Further when I use a formula for rectangle's area =L*B, where both lenght and breadth is present. But in case of circle I don't have a II(pie) anywhere. Why do we use this. What is the significance of II (pie). Why are you calculating the circumference? Hi Bunuel, I am calculating the circumference because I know the area of the rectangular (ignoring the height 15 cm as it is common to both can and carton). Once I know the area, I can divide the area by circumference of the circle to know the no of cans.



Math Expert
Joined: 02 Sep 2009
Posts: 49909

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
27 Apr 2013, 05:32
davidfrank wrote: Bunuel wrote: davidfrank wrote: I know the measurement of the carton, which is 48*32. Now the can's radius is 4 cm. Although the height of the carton is the same as the height of the cans i.e. 15, which I am ignoring as it will eventually cancel out in the calculation. My question is around the solution that is provided in the O.G. They have simply divided the length of the carton by diameter and width by diameter and then further multiplied the result.
(48/8)*(32/8) =6*4 =24.
Btw I got the right answer since its a DS problem. I am worried coz had this been a p.s problem, I might have got this one wrong. Now the way I would have solved this is
1st find the circumference of the circle (eliminating the height as the it is same). 2IIr=2*22/7*4 and then divided it by (48*32)/(176/7). My answer in this case is different from the OA =61.09
Why II (pie) was not considered. Why circumference was not considered instead of diameter. I failed to understand this. Can you please explain this.
Further when I use a formula for rectangle's area =L*B, where both lenght and breadth is present. But in case of circle I don't have a II(pie) anywhere. Why do we use this. What is the significance of II (pie).
Why are you calculating the circumference? Hi Bunuel, I am calculating the circumference because I know the area of the rectangular (ignoring the height 15 cm as it is common to both can and carton). Once I know the area, I can divide the area by circumference of the circle to know the no of cans. It seems that you don't understand the question. You need neither circumference of the cans nor the area. Simpler example might help: Attachment:
Untitled.png [ 10.24 KiB  Viewed 10583 times ]
The carton is 16 centimeters long and 16 centimeters wide. If the diameter of the cans is 8 centimeters, how many cans can be placed in the carton?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 12 Feb 2012
Posts: 125

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
05 Oct 2014, 19:40
When I did this problem, I inadvertinly read over the specification desigmating, width, length and height. In this case 15 was the height, allowing us to cram the most amount of cyclinder cans.
Here is my question, if height was not deginated as 15 in the case, would the solution be E? ie, we have the 15×32×48 dimensions but we don't know what is length, width, height. E is what I came up with.
Posted from my mobile device



Manager
Joined: 24 May 2013
Posts: 79

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
15 Mar 2016, 23:17
We only need the radius of the can to answer the question. Both the statements give the radius of the cans . So both are sufficient. D is the answer.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
09 Aug 2016, 13:47
Quote: Attachment: Carton.png The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k? (1) Each of the cans has a radius of 4 centimeters. (2) Six of the cans fit exactly along the length of the carton. We are given that a rectangular carton has a length of 48 cm, a width of 32 cm, and a height of 15 cm. We are also given that there are k identical cylindrical cans standing upright in this carton, and each can has a height of 15 cm. We need to determine the value of k, or the total number of cans in the carton. Because we have the dimensions of the carton, if we are able to determine the diameter of each can, then we will be able to determine the value of k. Statement One Alone:Each of the cans has a radius of 4 centimeters. Since the diameter is twice the radius we know that the diameter of each can is 8 cm. This is enough information to determine how many cans fit in the carton. Although we do not have to determine the actual value of k (because this is a data sufficiency problem), let’s determine it anyway. Since the length of the carton is 48 cm we could fit 48/8 = 6 cans along the length of the carton, and since the width of the carton is 32 cm, we could fit 32/8 = 4 cans along the width of the carton. Thus the carton could hold a total of 6 x 4 = 24 cans. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E. Statement Two Alone:Six of the cans fit exactly along the length of the carton. In a similar fashion to the process used in statement one, we can use the information in statement two to determine the diameter of each can. (Length of carton)/(diameter of each can) = number of cans that fit along the length of the carton 48/d = 6 48 = 6d d = 8 Since we have the diameter of each can, we have enough information to determine how many total cans fit in the carton. Statement two alone is also sufficient to answer the question. The answer is D. Note that because we have the length of the carton as 48 centimeters, statements 1 and 2 are giving us the same information – the length of the diameter or radius of each can. Whenever the two statements give the same information, the answer has to be D or E. It can’t be A or B because if one statement is sufficient (or insufficient), the other is too. It can’t be C because neither statement is adding information to the other. So as soon as we realized that A was sufficient in this question, we would know the answer is D.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 09 Mar 2011
Posts: 3

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
17 Mar 2018, 04:26
in statement B, its no where mentioned that radius is integer hence ans cant be D



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
17 Mar 2018, 10:55
vipulgoyal wrote: in statement B, its no where mentioned that radius is integer hence ans cant be D Hello Yes its not mentioned in statement 2 that radius is an integer. But thats not an issue. Applying the logic in statement 2, gives us the radius, which is in fact an integer only (4 cm, which is same as that mentioned in statement 1). So there is no problem.



Senior Manager
Joined: 02 Apr 2014
Posts: 471

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
17 Mar 2018, 22:28
Hi Bunuel, I have a question, because it is mentioned in the question as "filled to capacity", we are considering the cans are standing upright against the surface with dimensions 48 * 32 (as the height exactly matches height of the carton to fill it completely), and find the answer as D. Had the question not given as "filled to capacity", we could also consider the cans standing upright against surfaces 48 * 15 or 32 * 15, in which cases, we will get different values of k and answer will be E. Is my understanding correct? Please help. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 49909

Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet
[#permalink]
Show Tags
18 Mar 2018, 01:02
hellosanthosh2k2 wrote: Hi Bunuel, I have a question, because it is mentioned in the question as "filled to capacity", we are considering the cans are standing upright against the surface with dimensions 48 * 32 (as the height exactly matches height of the carton to fill it completely), and find the answer as D. Had the question not given as "filled to capacity", we could also consider the cans standing upright against surfaces 48 * 15 or 32 * 15, in which cases, we will get different values of k and answer will be E. Is my understanding correct? Please help. Thanks The dimensions of the carton are 48 centimeters long, 32 centimeters wide, and 15 centimeters high. This implies that the carton is standing on 48*32 face. In addition we are told that the cans of stand upright in rows and columns, so they stand on circular base.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: The inside of a rectangular carton is 48 centimeters long, 32 centimet &nbs
[#permalink]
18 Mar 2018, 01:02






