B 64 is the answer
Width of patio is x+5
area of walkway = (3x+5)^2 - (x+5)^2 = 132
solving we get x = 3
area of patio = (x+5)^2 = 8^2 = 64
Neo
2 min question again :)
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lets say length of square patio=y
y=x+5--------------------------eqn1
Now, (y+2x)^2-y^2=132 ---given
4x^2+4xy=132 => x^2+xy=33
=x^2+x(x+5)=33
=2x^2+5x-33=0
By solving it we get x=3 & -22/4
so, x=3
therefore, y=3+5=8
area of patio=8^2=64
y=x+5--------------------------eqn1
Now, (y+2x)^2-y^2=132 ---given
4x^2+4xy=132 => x^2+xy=33
=x^2+x(x+5)=33
=2x^2+5x-33=0
By solving it we get x=3 & -22/4
so, x=3
therefore, y=3+5=8
area of patio=8^2=64
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Stuart@KaplanGMAT
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The answer choices are concrete numbers and we have a complicated word problem - great candidate for backsolving.
The answer choices are:
a) 56
b) 64
c) 68
d) 81
e) 100
First, let's use some common sense. It's a square patio, so the area is almost certainly going to be a perfect square: eliminate (a) and (c).
We're left with:
b) 64
d) 81
e) 100
Using the Kaplan method for backsolving, when we have 3 choices we always check the middle one first. So, let's assume that the area of the square patio is 81.
Therefore, the patio is 9 * 9 and the area of the big square is 17 * 17 (if the patio is 9 metres wide and is 5 metres wider than the walkway, the walkway is (9-5)=4 metres wide which means that the entire squre is (9+4+4)=17 metres wide).
Well, 17*17 is 289. The area of the walkway is the area of the big square minus the area of the small square, or:
289 - 81 = 208.
Is 208 the happy ending to the story? NO - we wanted 132.
Therefore, (b) is wrong. Further, since we got too much area, we need to reduce the dimensions, so we can also eliminate (e) 100.
The only answer left is 64: choose (b).
* * *
Note: if the algebra jumps out at you, then it will usually be quicker than backsolving. If the algebra doesn't jump out at you, then backsolving is a fantastic way to avoid setting up complex equations, since we work our way through the story using real numbers instead of variables.
Like any other technique, backsolving requires practice. The first few times you use it, backsolving will be VERY slow. However, if you perfect your understanding of how to backsolve effectively, it can be an amazing test day tool.
The answer choices are:
a) 56
b) 64
c) 68
d) 81
e) 100
First, let's use some common sense. It's a square patio, so the area is almost certainly going to be a perfect square: eliminate (a) and (c).
We're left with:
b) 64
d) 81
e) 100
Using the Kaplan method for backsolving, when we have 3 choices we always check the middle one first. So, let's assume that the area of the square patio is 81.
Therefore, the patio is 9 * 9 and the area of the big square is 17 * 17 (if the patio is 9 metres wide and is 5 metres wider than the walkway, the walkway is (9-5)=4 metres wide which means that the entire squre is (9+4+4)=17 metres wide).
Well, 17*17 is 289. The area of the walkway is the area of the big square minus the area of the small square, or:
289 - 81 = 208.
Is 208 the happy ending to the story? NO - we wanted 132.
Therefore, (b) is wrong. Further, since we got too much area, we need to reduce the dimensions, so we can also eliminate (e) 100.
The only answer left is 64: choose (b).
* * *
Note: if the algebra jumps out at you, then it will usually be quicker than backsolving. If the algebra doesn't jump out at you, then backsolving is a fantastic way to avoid setting up complex equations, since we work our way through the story using real numbers instead of variables.
Like any other technique, backsolving requires practice. The first few times you use it, backsolving will be VERY slow. However, if you perfect your understanding of how to backsolve effectively, it can be an amazing test day tool.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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Stuart Kovinsky wrote:The answer choices are concrete numbers and we have a complicated word problem - great candidate for backsolving.
The answer choices are:
a) 56
b) 64
c) 68
d) 81
e) 100
First, let's use some common sense. It's a square patio, so the area is almost certainly going to be a perfect square: eliminate (a) and (c).
We're left with:
b) 64
d) 81
e) 100
Using the Kaplan method for backsolving, when we have 3 choices we always check the middle one first. So, let's assume that the area of the square patio is 81.
Therefore, the patio is 9 * 9 and the area of the big square is 17 * 17 (if the patio is 9 metres wide and is 5 metres wider than the walkway, the walkway is (9-5)=4 metres wide which means that the entire square is (9+4+4)=17 metres wide).
Well, 17*17 is 289. The area of the walkway is the area of the big square minus the area of the small square, or:
289 - 81 = 208.
Is 208 the happy ending to the story? NO - we wanted 132.
Therefore, (b) is wrong. Further, since we got too much area, we need to reduce the dimensions, so we can also eliminate (e) 100.
The only answer left is 64: choose (b).
* * *
Note: if the algebra jumps out at you, then it will usually be quicker than backsolving. If the algebra doesn't jump out at you, then backsolving is a fantastic way to avoid setting up complex equations, since we work our way through the story using real numbers instead of variables.
Like any other technique, backsolving requires practice. The first few times you use it, backsolving will be VERY slow. However, if you perfect your understanding of how to backsolve effectively, it can be an amazing test day tool.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Stuart - I always seem to realize a good back-solved problem after I have already wasted a bunch of time.
You said this was a good candidate because of concrete numbers and a "complicated" word problem.
How do you usually identify a good problem like this immediately?
You said this was a good candidate because of concrete numbers and a "complicated" word problem.
How do you usually identify a good problem like this immediately?
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The main criterion for backsolving is numbers in the choices. If you see variables or percents, backsolving will be a lot tougher.zacharyz wrote:Stuart - I always seem to realize a good back-solved problem after I have already wasted a bunch of time.
You said this was a good candidate because of concrete numbers and a "complicated" word problem.
How do you usually identify a good problem like this immediately?
Next we look at the question itself. To backsolve, we generally need 1 of two scenarios:
(1) word problem with concete ending and a simple question
(e.g. "what is the value of x" or "how much does bob weigh" vs "what's the difference between x and y" or "how much money will bob have left at the end of the month"); or
(2) equation to solve with a simple question
(e.g. "if |5x - 8| = 10, what's the value of x")
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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when I read this problem, first thoughts that came into mind:
1) the patio is a square, so the area is likely a perfect square (elim a/c)
2) the big area (patio + walkway) is also a square, so that area will likely be a perfect square as well, which means that the patio area + 132 is likely a perfect square (elim d/e)
we're left with b) 64.
then just double check the answer.
1) the patio is a square, so the area is likely a perfect square (elim a/c)
2) the big area (patio + walkway) is also a square, so that area will likely be a perfect square as well, which means that the patio area + 132 is likely a perfect square (elim d/e)
we're left with b) 64.
then just double check the answer.
I beat the GMAT! 760 (Q49/V44)
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VP_RedSoxFan
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My only caution about backsolving is when we start with assumptions like, since the patio is square, the answer must likely be a perfect square. In this problem, x can be solved for as x=3 so it works out, but a different solution of x could have actually precluded it from being a square. Then we would have spent a minute or 2 testing 3 answers that couldn't be correct, finish without a conclusive answer and then retest assuming we'd made an error somewhere in those 3 even though our error could have been in assuming it was a square in the first place.
I also am leery of backsolving as a main strategy because it lends itself to a lot of computation, and, thus, careless errors.
Learning to move through the algebra on a problem like this (the hardest part is factoring 4x^2+5x-66=0 into (4x+22)(x-3)=0) is a worthwhile endeavor--one that pays off on test day for this and other problems like it. I'd guess that without a strong command of algebra and problem solving skills like the ones tested on this problem, you have a much lower ceiling for a overall score.
Just my humble opinion....
I also am leery of backsolving as a main strategy because it lends itself to a lot of computation, and, thus, careless errors.
Learning to move through the algebra on a problem like this (the hardest part is factoring 4x^2+5x-66=0 into (4x+22)(x-3)=0) is a worthwhile endeavor--one that pays off on test day for this and other problems like it. I'd guess that without a strong command of algebra and problem solving skills like the ones tested on this problem, you have a much lower ceiling for a overall score.
Just my humble opinion....
Ryan S.
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AleksandrM
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VP_RedSoxFan wrote:My only caution about backsolving is when we start with assumptions like, since the patio is square, the answer must likely be a perfect square. In this problem, x can be solved for as x=3 so it works out, but a different solution of x could have actually precluded it from being a square. Then we would have spent a minute or 2 testing 3 answers that couldn't be correct, finish without a conclusive answer and then retest assuming we'd made an error somewhere in those 3 even though our error could have been in assuming it was a square in the first place.
I also am leery of backsolving as a main strategy because it lends itself to a lot of computation, and, thus, careless errors.
Learning to move through the algebra on a problem like this (the hardest part is factoring 4x^2+5x-66=0 into (4x+22)(x-3)=0) is a worthwhile endeavor--one that pays off on test day for this and other problems like it. I'd guess that without a strong command of algebra and problem solving skills like the ones tested on this problem, you have a much lower ceiling for a overall score.
Just my humble opinion....
I agree with Ryan here- actually, I will be much less diplomatic about this strategy. Backsolving is normally a huge waste of time on the GMAT- you often end up solving the same problem two or three times, when algebra would get you to the solution the first time. If you can do the algebra, you'll do much better on the test. Backsolving only lends itself to word or algebra problems with numerical answers, and you won't see many of those past the 550 level; it's a low-level technique, and should only be viewed as a fallback strategy. If you're stuck, definitely use it, but it should not be the first thing a well-prepared GMAT taker should think to do. If you're aiming for a 700, these kinds of 'tricks' won't get you there; you need to know some math.
The problem in the OP does not look like a real GMAT problem (the algebraic result is too complicated to solve quickly)- it reads like a test prep company problem. Test prep company questions are often not a good guide to what you'll see on the real GMAT test- companies manufacture problems to illustrate the efficacy of their strategies. Look at the OG or the GMATPrep software, and judge for yourself how useful backsolving is- there are close to no problems, at least past the easy stage, from official materials that are best solved by backsolving (excluding problems which explicitly force you to backsolve, like 'which of the following is largest?').
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I'm going to vehemently disagree.
Backsolving is a fantastic strategy. I'm great at math, yet there are still many questions that I find it quicker to backsolve. The answers are incredibly powerful tools on a multiple choice test and anyone who ignores them wilL NOT hit his or her highest potential score.
Now, backsolving isn't the right choice for every person on every backsolvable question. Whether to backsolve a particular problem will depend on whether the algebra jumps off the page at you and how much more comfortable you are with concrete numbers than abstract variables. However, the more you practice backsolving, just like any other strategy with which you're not familiar, the better you'll become at it and the more value if will hold on test day.
No legitimate test prep company will say "this is how you MUST attack this particular type of question". Our goal (at least speaking for Kaplan) is to provide our students with as many tools as possible for test day and to encourage our students to practice using every one of those tools with the end goal of being able to look at EVERY question on the GMAT and say "this is similar to a problem I did while practicing... in practice, method X was the best way for me to solve it... therefore, I'll use method X on this question".
The difference between a marginal score and a competitive one is often merely how long it takes you to make that decision and how often you make the best choice.
Backsolving is a fantastic strategy. I'm great at math, yet there are still many questions that I find it quicker to backsolve. The answers are incredibly powerful tools on a multiple choice test and anyone who ignores them wilL NOT hit his or her highest potential score.
Now, backsolving isn't the right choice for every person on every backsolvable question. Whether to backsolve a particular problem will depend on whether the algebra jumps off the page at you and how much more comfortable you are with concrete numbers than abstract variables. However, the more you practice backsolving, just like any other strategy with which you're not familiar, the better you'll become at it and the more value if will hold on test day.
No legitimate test prep company will say "this is how you MUST attack this particular type of question". Our goal (at least speaking for Kaplan) is to provide our students with as many tools as possible for test day and to encourage our students to practice using every one of those tools with the end goal of being able to look at EVERY question on the GMAT and say "this is similar to a problem I did while practicing... in practice, method X was the best way for me to solve it... therefore, I'll use method X on this question".
The difference between a marginal score and a competitive one is often merely how long it takes you to make that decision and how often you make the best choice.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
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getneonow
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AleksAleksandrM wrote:getneo,
Why (3x - 5)^2 ... specifically why "3x"
Given that width of walkway = x
and width of patio = x+5
I hope above two are clear.
Now if we want to calculate the are of walkway = area of outer square - area of inner square.
area of any square = side * side
side of outer square = x+ (x+5) +x = 3x+5
side of inner square(PATIO) = x+5
Width of patio is x+5
area of walkway = (3x+5)^2 - (x+5)^2 = 132
solving we get x = 3
area of patio = (x+5)^2 = 8^2 = 64
Hope this helps
Neo
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That doesn't surprise me!Stuart Kovinsky wrote:I'm going to vehemently disagree.
The answers are often very valuable- we agree there- but that's not, in most cases, because they enable backsolving. There are many other ways to use answer choices to your advantage on the GMAT, which I may go into in another post.Stuart Kovinsky wrote: Backsolving is a fantastic strategy. I'm great at math, yet there are still many questions that I find it quicker to backsolve. The answers are incredibly powerful tools on a multiple choice test and anyone who ignores them wilL NOT hit his or her highest potential score.
Is backsolving a 'fantastic strategy'? I said in my last post that it is not normally a good strategy to use at the higher levels of the test. Take a sample of difficult GMAT questions- I just looked at questions 200 through 249 in the Problem Solving section of the orange Official Guide. Of these 50 questions:
- 14 questions could, in theory, be solved by backsolving;
- the only question where backsolving seems a good approach is number 200, and even there, the algebra is simple: the time required is equal either way. There are three that some might find debatable:
- Someone stuck on question 223 might backsolve, but this is such a common question type that a well-prepared test-taker should have a much quicker strategy here (subtract the speeds);
- Question 228 can be backsolved, but the answer choices are the only plausible answers, so seeing them is not very helpful;
- Question 232 can be backsolved, but the algebra is very fast;
- On questions 205, 210, 211, 213, 220, 222, 235, 237, 238, and 240, if you choose to backsolve, you are spending more time than you should. In these questions, if you backsolve, then for each answer choice you need to test you are doing the same steps (in reverse) as you would do if you solved the question algebraically. The algebra gives you the answer on the first try, while by backsolving you may need to do the same question several times over. Worse still, on some questions this can lead to very time-consuming calculations (213, 238, among others).
This is why I said, in my previous post, that backsolving is a low-level strategy; it can be used to answer questions, but it is rarely the best approach, at least if you're aiming for an elite GMAT score. There's no harm in learning how to do it- there's really nothing to learn. And backsolving is a good fallback if you can't do a question directly- much better to backsolve than to guess randomly, of course. But if you can do a question directly, it is almost always best to do so on difficult GMAT questions.
More importantly, however- going by the Official Guide, roughly three quarters of hard GMAT problems are entirely immune to backsolving. For these, you need to have some conceptual understanding of mathematics, need to be able to handle abstraction, and need to be able to set up equations. To do well on these questions, you need to learn math- 'tricks' won't help.
