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ELEMENTARY, MY DEAR WATSON!

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ELEMENTARY, MY DEAR WATSON! [#permalink]

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New post 29 Oct 2014, 07:29
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FROM Veritas Prep Blog: Elementary, My Dear Watson!
Image
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.

Image

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.

Image

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 8-15-17 pythagorean triplet? (the third triplet after 3-4-5 and 5-12-13)

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 3-4-5 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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135275 [4], given: 12679

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Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135275 [0], given: 12679

Re: ELEMENTARY, MY DEAR WATSON! [#permalink]

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New post 01 Oct 2017, 06:47
Bunuel wrote:
FROM Veritas Prep Blog: Elementary, My Dear Watson!
Image
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.

Image

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.

Image

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 8-15-17 pythagorean triplet? (the third triplet after 3-4-5 and 5-12-13)

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 3-4-5 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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135275 [0], given: 12679

Re: ELEMENTARY, MY DEAR WATSON!   [#permalink] 01 Oct 2017, 06:47
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ELEMENTARY, MY DEAR WATSON!

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