Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44400

ELEMENTARY, MY DEAR WATSON! [#permalink]
Show Tags
29 Oct 2014, 07:29
4
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
FROM Veritas Prep Blog: Elementary, My Dear Watson!

While eagerly awaiting the kick off of season 3 of BBC’s Sherlock, let’s put our time to good use. Though we have already spent a lot of it speculating over what really happened to Sherlock (HOW did he come back?!), perhaps we can take a leaf out of his book and learn to notice little things in whatever is leftover. There is a good reason to do that – there are little clues in some questions that the test maker unwittingly leaves to bring clarity to the question. If we understand those clues, a seemingly mysterious problem could be easily unraveled. Let us show you with an example.
Question: Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, what is the difference in the distance traveled by the two?
(A) 20
(B) 40
(C) 80
(D) 120
(E) 140
Solution: The first thing we do in these “direction” questions is draw the diagram. But there is a problem here: how do we decide the orientation of the rectangle? It could be either of these two.
A few things help us decide this. There are two definitions of length:
1. Length is the longest side of the rectangle.
2. Width is from side to side and length is whatever width isn’t (i.e. the side from up to down in a rectangle) (this definition is less embraced than the first one)
If the side from up to down is the longest side, then there is no conflict.
Keeping this in mind, when drawing the figure, given that length is the longer of the two, one could make the rectangle on the left and there will be no conflict. But the question maker may not want to take for granted that you know this.
So he/she leaves a clue – the question mentions that ‘Jacob walks 180 ft down the west side of the field’. There needs to be at least 180 ft on the west side of the field for him to travel that much. So the orientation on the left makes sense. This is something the question maker would have put to try to give you a hint of the orientation. Now that we know what our diagram should look like, we can proceed to solve this question.
If you just remember some of your pythagorean triplets, this question can be solved in moments (and that’s why we suggest you to remember them!) If not, it would involve some calculations.
QR = 160, RS = 300
So QR:RS = 8:15
Remember 81517 pythagorean triplet? (the third triplet after 345 and 51213)
Since the two sides are in the ratio 8:15, the hypotenuse must be 17. The common multiplier is 20 so QS should be 17*20 = 340
Therefore, Peter traveled 340 feet.
TP = 120, PS = 160
TP:PS = 3:4
Does it remind you of 345 triplet?
120 is 3*40 and 160 is 4*40 so TS will be 5*40 = 200
So Jacob traveled a total distance of 180 + 200 = 380 feet.
Difference between the distance traveled = 380 – 340 = 40 feet
Note: The following triplets come in handy: (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) and (9, 40, 41)
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMATfor Veritas Prep and regularly participates in content development projects such as this blog!

ForumBlogs  GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
_________________
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





Math Expert
Joined: 02 Sep 2009
Posts: 44400

Re: ELEMENTARY, MY DEAR WATSON! [#permalink]
Show Tags
01 Oct 2017, 06:47
Bunuel wrote:
FROM Veritas Prep Blog: Elementary, My Dear Watson!

While eagerly awaiting the kick off of season 3 of BBC’s Sherlock, let’s put our time to good use. Though we have already spent a lot of it speculating over what really happened to Sherlock (HOW did he come back?!), perhaps we can take a leaf out of his book and learn to notice little things in whatever is leftover. There is a good reason to do that – there are little clues in some questions that the test maker unwittingly leaves to bring clarity to the question. If we understand those clues, a seemingly mysterious problem could be easily unraveled. Let us show you with an example.
Question: Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, what is the difference in the distance traveled by the two?
(A) 20
(B) 40
(C) 80
(D) 120
(E) 140
Solution: The first thing we do in these “direction” questions is draw the diagram. But there is a problem here: how do we decide the orientation of the rectangle? It could be either of these two.
A few things help us decide this. There are two definitions of length:
1. Length is the longest side of the rectangle.
2. Width is from side to side and length is whatever width isn’t (i.e. the side from up to down in a rectangle) (this definition is less embraced than the first one)
If the side from up to down is the longest side, then there is no conflict.
Keeping this in mind, when drawing the figure, given that length is the longer of the two, one could make the rectangle on the left and there will be no conflict. But the question maker may not want to take for granted that you know this.
So he/she leaves a clue – the question mentions that ‘Jacob walks 180 ft down the west side of the field’. There needs to be at least 180 ft on the west side of the field for him to travel that much. So the orientation on the left makes sense. This is something the question maker would have put to try to give you a hint of the orientation. Now that we know what our diagram should look like, we can proceed to solve this question.
If you just remember some of your pythagorean triplets, this question can be solved in moments (and that’s why we suggest you to remember them!) If not, it would involve some calculations.
QR = 160, RS = 300
So QR:RS = 8:15
Remember 81517 pythagorean triplet? (the third triplet after 345 and 51213)
Since the two sides are in the ratio 8:15, the hypotenuse must be 17. The common multiplier is 20 so QS should be 17*20 = 340
Therefore, Peter traveled 340 feet.
TP = 120, PS = 160
TP:PS = 3:4
Does it remind you of 345 triplet?
120 is 3*40 and 160 is 4*40 so TS will be 5*40 = 200
So Jacob traveled a total distance of 180 + 200 = 380 feet.
Difference between the distance traveled = 380 – 340 = 40 feet
Note: The following triplets come in handy: (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) and (9, 40, 41)
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMATfor Veritas Prep and regularly participates in content development projects such as this blog!

ForumBlogs  GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
_______________________________ BUMP
_________________
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: ELEMENTARY, MY DEAR WATSON!
[#permalink]
01 Oct 2017, 06:47






