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THIS WEEK’S FREE DON’T SOLVE PROBLEM ON EQUATIONS

admin — Wed, 10 Mar 2010 13:22:07 +0000

Don’t Solve are Smart Math problems attempted without solving. By using simple logic and smart techniques, answers to seemingly complex Math problems can be easily found in a matter of seconds… without actually solving the problem! Don’t believe it? Read below to see it for yourself!

Anyone can benefit by learning better Math. Whether you are a student, a parent, a teacher or simple a casual Internet surfer, this will change your outlook for Math – guaranteed! Whether you are taking any Math test or even training others for a Math test, these Math techniques will boost your confidence as well as the score. Don’t take GRE, GMAT, SAT or any other similar test without LazyMaths.com. Our students have reported significant increase in their quant scores in these tests.

Know more about Don’t Solve here

Every week we publish 1 FREE Don’t Solve problem. To learn all the hundreds of math techniques, sign up with LazyMaths.com. When you sign up and become a member, you can access math techniques in Algebra, Geometry, Ratio Proportion, Averages, Time Speed & Distance and many more areas. You can also interact with other users, leave comments, ask questions and rate every problem!

Here is this week’s FREE Don’t Solve problem…

Problem

Find the value of ‘a’ in .

a. 4

b. 2

c. 1

d. 3

e. 0

Usual Method

() = 12

= 1

a = 0

(Ans: e)

Estimated Time to arrive at the answer = 75 seconds.

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Smart Technique

Simply look at the options and start substituting the values in the expressions and just check which one satisfies the equation Also, remember to start substituting with the value that is easiest of all to substitute. In this case, for example, the easier values are ‘0’ and ‘1’. You would notice that ‘0’ satisfies the equation as follows:

Hence option ‘e’.

(Ans: e)

Estimated Time to arrive at the answer = 10 seconds.

Tell us what you think about the techniques used to solve this problem. Does this help in making math easy? Save time?

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NOTE: We publish one FREE problem every Wednesday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THIS WEEK’S FREE SPEED MATH SHORTCUT – 98989×4

admin — Sun, 07 Mar 2010 18:19:10 +0000

Zappers are Speed Math shortcuts that help solve seemingly complex Math problems in a matter of seconds… without using a calculator!

Anyone can benefit by learning better Math. Whether you are a student, a parent, a teacher or simple a casual Internet surfer. This will change your outlook for Math – guaranteed! Whether you are taking any Math test or even training others for a Math test, these Math shortcuts will boost your confidence as well as score. Don’t take GRE, GMAT, SAT or any other similar test without LazyMaths.com. Our students have reported significant increase in their quant scores in these tests.

Know more about Zappers here.

Every week we publish 1 FREE Zapper. To learn all the hundreds of math shortcuts, sign up with LazyMaths.com. When you sign up and become a member, you can access hundreds of math shortcuts, download practice sheets, leave comments, ask questions and rate every shortcut!

Here is this week’s FREE Zapper…

Tell us what you think about this shortcut. Does this help in making math easy? Save time?

Feel free to suggest any new shortcuts or share your comments. If you like this site, share it with your friends.

NOTE: We publish one FREE shortcut every Sunday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THIS WEEK’S FREE DON’T SOLVE PROBLEM ON RATIO PROPORTION

admin — Wed, 03 Mar 2010 13:17:53 +0000

Know more about Don’t Solve here

Here is this week’s FREE Don’t Solve problem…

Problem

3 men and 6 women can dig a well in 4 days. 5 men and 4 women take 3 days. How many days would 8 women and 1 man take?

a. 6 days

b. 8 days

c. 10 days

d. 4 days

e. 9 days

Usual Method

Let ‘m’ be the fraction be the amount of work done by 1 man in 1 day and ‘w’ be the fraction of work done by 1 woman in 1 day.

3m + 6w = 1/4

12 m + 24 w = 1 …… Eq. 1.

Similarly,

5m + 4w = 1/3

15m + 12w = 1 …… Eq. 2.

Solving both equation 1 and 2 simultaneously we get

18m = 1 and 72w = 1

m = and w =

8w + 1m =

Hence, 6 days.

(Ans: a)

Estimated Time to arrive at the answer = 120 seconds.

Smart Technique

If 3 men and 6 women take 4 days, hypothetically, 1.5 men and 3 women will take 8 days. Hence, 1 man and 8 women will obviously take less than 8 days. Also, 1 man and 8 women will also take more than 4 days; hence the answer lies between 8 days and 4 days i.e. 6 days.

(Ans: a)

Estimated Time to arrive at the answer = 5 seconds.

Tell us what you think about the techniques used to solve this problem. Does this help in making math easy? Save time?

Feel free to suggest any new shortcuts or share your comments. If you like this site, share it with your friends.

NOTE: We publish one FREE problem every Wednesday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THIS WEEK’S FREE SPEED MATH SHORTCUT – 89×95

admin — Sun, 28 Feb 2010 18:14:34 +0000

Zappers are Speed Math shortcuts that help solve seemingly complex Math problems in a matter of seconds… without using a calculator!

Know more about Zappers here.

Here is this week’s FREE Zapper…

Tell us what you think about this shortcut. Does this help in making math easy? Save time?

Feel free to suggest any new shortcuts or share your comments. If you like this site, share it with your friends.

NOTE: We publish one FREE shortcut every Sunday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THIS WEEK’S FREE DON’T SOLVE PROBLEM ON RATIO PROPORTION

admin — Wed, 24 Feb 2010 13:14:22 +0000

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Here is this week’s FREE Don’t Solve problem…

Problem

In an alloy of three metals A, B and C, the quantity of metal A is 4/5th of B and that of B is 3/4th of C. What is the quantity in lb of each metal in 47 lbs of the alloy? (In the order of A, B and C.)

a. 13, 22, 12

b. 12, 13, 22

c. 12, 15, 20

d. 20, 15, 12

e. 10, 20, 18

Usual Method

A = 4/5 B B = 3/4 C

5A = 4B 4B = 3C

A : B = 4 : 5 B : C = 3 : 4

A : B : C

4 : 5

3 : 4

12 : 15 : 20

Also, 12 + 15 + 20 = 47 lbs

Hence, A = 12 lbs, B = 15 lbs and C = 20 lbs.

(Ans: c)

Estimated Time to arrive at the answer = 60 seconds.

Smart Technique

The first step is to eliminate those options whose sum 47. Thus option ‘e’ is eliminated as sum of 10 + 20 + 18 = 48.

The next step is to identify the metal with maximum or minimum quantity. Because A = 4/5 B and B = 3/4 C; the metal C is of maximum quantity and A is of minimum quantity. Thus options ‘a’ and ‘d’ are eliminated. This leaves us with options ‘b’ and ‘c’ only. Since, A = 4/5 B; 5A = 4B.

For option ‘b’, 5 x 12 4 x 13, hence ‘b’ is also eliminated. Thus answer is option ‘c’.

(Ans: c)

Estimated Time to arrive at the answer = 15 seconds.

Tell us what you think about the techniques used to solve this problem. Does this help in making math easy? Save time?

Feel free to suggest any new shortcuts or share your comments. If you like this site, share it with your friends.

NOTE: We publish one FREE problem every Wednesday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THIS WEEK’S FREE SPEED MATH SHORTCUT – 73321×9

admin — Sun, 21 Feb 2010 18:10:59 +0000

Zappers are Speed Math shortcuts that help solve seemingly complex Math problems in a matter of seconds… without using a calculator!

Know more about Zappers here.

Here is this week’s FREE Zapper…

Tell us what you think about this shortcut. Does this help in making math easy? Save time?

Feel free to suggest any new shortcuts or share your comments. If you like this site, share it with your friends.

NOTE: We publish one FREE shortcut every Sunday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THIS WEEK’S FREE DON’T SOLVE PROBLEM ON BASIC ARITHMETIC

admin — Wed, 17 Feb 2010 13:09:34 +0000

Know more about Don’t Solve here

Here is this week’s FREE Don’t Solve problem…

Problem

If means ; find the value of 3.124*1.39.

a. 2.41324

b. 3.24026

c. 4.00236

d. 2.41026

e. 2.313456

Usual Method

Substituting the values of ‘x’ and ‘y’ according to the data given, we get

i.e.

= 2.41026

(Ans: d)

Estimated Time to arrive at the answer = 90 seconds as this is a calculation intensive problem.

Smart Technique

Just get to the ‘’ level. Note that the product of these two numbers should be 2+3 = 5 digits after the decimal point. This eliminates option ‘e’.

Also, the product of the last digits is ‘6’ (9 x 4 = 36). Hence, ‘6’ should be the last digit of the answer. This eliminates option ‘a’.

Also, note that 13 x 17 > 200. Hence, the answer should be a number starting with 2.something…

Hence, the answer is option ‘d’.

(Ans: d)

Estimated Time to arrive at the answer = 10 seconds

Tell us what you think about the techniques used to solve this problem. Does this help in making math easy? Save time?

Feel free to suggest any new shortcuts or share your comments. If you like this site, share it with your friends.

NOTE: We publish one FREE problem every Wednesday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THIS WEEK’S FREE SPEED MATH SHORTCUT – 18^3

admin — Sun, 14 Feb 2010 18:03:05 +0000

Zappers are Speed Math shortcuts that help solve seemingly complex Math problems in a matter of seconds… without using a calculator!

Know more about Zappers here.

Here is this week’s FREE Zapper…

Tell us what you think about this shortcut. Does this help in making math easy? Save time?

Feel free to suggest any new shortcuts or share your comments. If you like this site, share it with your friends.

NOTE: We publish one FREE shortcut every Sunday. It auto expires after 1 month. Become a Member to learn hundreds of shortcuts and techniques.

THE ULTIMATE COLLECTION OF EVERY KNOWN TESTS OF DIVISIBILITY

admin — Wed, 10 Jun 2009 02:24:31 +0000

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After the most successful and very useful article on THE ULTIMATE GUIDE TO NUMBER CLASSIFICATION, LazyMaths.com is pleased to offer another path breaking article – THE ULTIMATE COLLECTION OF EVERY KNOWN TESTS OF DIVISIBILITY.

As a part of any speed math exam like GMAT, GRE or CAT, if you are trying to find out whether that number is evenly divisible without actually dividing it, then use these tests of divisibility. Learn these tests and save yourself precious time.

Divisor	Divisibility condition	Examples
1	Automatic	Every number is divisible by 1
2	The last digit is even (0,2,4,6 or 8 )	1294: 4 is even
3	The sum of digits is divisible by 3.	405: 4 + 0 + 5 = 9, which clearly is divisible by 3.
4	The number formed by the last two digits is divisible by 4.	40832: 32 is divisible by 4.
5	The last digit is 0 or 5.	490: the last digit is 0.
6	It is divisible by 2 and 3.	1,458: 1 + 4 + 5 + 8 = 18, 1 + 8 = 9, so it is divisible by 3 and the last digit is even, hence number is divisible 6.
7	If you double the last digit and subtract it from the rest of the number and the answer is divisible by 7.	483: 48 – (3 × 2) = 42 = 7 x 6.
8	The number formed by the last three digits is divisible by 8.	56: (5 × 2) + 6 = 16.
9	The sum of digits is divisible by 9.	2,880: 2 + 8 + 8 + 0 = 18: 1 + 8 = 9.
10	The number ends in 0.	130: the last digit is 0.
11	If you sum every second digit, and subtract all the other digits, the answer is divisible by 11.	918,082: 9 – 1 + 8 – 0 + 8 – 2 = 22.
12	The number is divisible by 3 and 4.	324: (32 × 2) − 4 = 60.
13	Add 4 times the last digit to the rest, the answer is divisible by 13.	637: 63 + (7 × 4) = 91, 9 + (1 × 4) = 13.
14	It is divisible by 2 and 7	224: it is divisible by 2 and by 7.
15	It is divisible by 3 and 5	390: it is divisible by 3 and by 5.
16	Sum the number with last two digits removed, times 4, plus the last two digits.	176: (1 × 4) + 76 = 80.
17	Subtract 5 times the last digit from the rest, the answer is divisible by 17.	221: 22 – (1 × 5) = 17.
18	It is divisible by 2 and 9.	342: it is divisible by 2 and by 9.
19	Add twice the last digit to the rest, the answer is divisible by 19.	437: 43 + (7 × 2) = 57.
20	The number formed by the last 2 digits is divisible by 20.	480: 80 is divisible by 20.
21	Subtract twice the last digit from the rest.	168: 16 – (8×2) = 0, 168 is divisible. 1050: 105 – (0×2) = 105, 10 – (5×2) = 0, 1050 is divisible.
23	Add 7 times the last digit to the rest.
25	The number formed by the last two digits is divisible by 25.	134,250: 50 is divisible by 25.
27	Since 37×27=999; the multiplier is one, taking three digits at-a-time. Sum the digits in blocks of three from right to left.	2,644,272: 2 + 644 + 272 = 918.
	Subtract 8 times the last digit from the rest.	621: 62 − (1×8) = 54.
29	Add three times the last digit to the rest.	261: 1×3=3; 3+26= 29
31	Subtract three times the last digit from the rest.
32	The number formed by the last five digits is divisible by 32, as follows:
	If the ten thousands digit is even, examine the number formed by the last four digits.	41,312: 1312.
	If the ten thousands digit is odd, examine the number formed by the last four digits plus 16.	254,176: 4176+16 = 4192.
	Add the last two digits to 4 times the rest.	1,312: (13×4) + 12 = 64.
33	Add 10 times the last digit to the rest.	627: 62 + 7 x 10 = 132, 13 + 2 x 10 = 33.
37	Sum the digits in blocks of three from right to left. Since 37×27=999; round up to 1000; drop the three zeros; the multiplier is one, taking three digits at-a-time. Add these products, going from right to left. If the result is divisible by 37, then the number is divisible by 37.	2,651,272: 2 + 651 + 272 = 925. 925/37=25, yes, divisible.
	Subtract 11 times the last digit from the rest.	925: 92 − (5×11) = 37.
39	Add 4 times the last digit to the rest.	351: 1×4=4; 4+35=39
41	Subtract 4 times the last digit from the rest.	738: 73 – 8 x 4 = 41.
43	Add 13 times the last digit to the rest.	36,249: 3624 + 9 x 13 = 3741, 374 + 1 x 13 = 387, 38 + 7 x 13 = 129, 12 + 9 x 13 = 129 = 43 x 3.
47	Subtract 14 times the last digit from the rest.	1,642,979: 164297- 9 x 14 = 164171, 16417 – 14 = 16403, 1640 – 3 x 14 = 1598, 159 – 8 x 14 = 47.
49	Add 5 times the last digit to the rest.	1,127: 112+(7×5)=147. 147: 14 + (7×5) = 49 Yes, divisible.
51	Subtract 5 times the last digit to the rest.
59	Add 6 times the last digit to the rest.	295: 5×6=30; 30+29=59
61	Subtract 6 times the last digit from the rest.
69	Add 7 times the last digit to the rest.	345: 5×7=35; 35+34=69
71	Subtract 7 times the last digit from the rest.
79	Add 8 times the last digit to the rest.	711: 1×8=8; 8+71=79
81	Subtract 8 times the last digit from the rest.
89	Add 9 times the last digit to the rest.	801: 1×9=9; 80+9=89
91	Subtract 9 times the last digit from the rest.
989	Divide the number of thousands by 989. Multiply the remainder by 11 and add to last 3 digits.	21758: 21/989 Remainder = 21, 21 x 11 = 231; 758 + 231=989

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PROVING APPROXIMATION WITH PRECISION

admin — Thu, 28 May 2009 15:52:09 +0000

The New York Times recently (Sep 16) published an interesting article – “Gut Instinct’s surprising role in Math”. The article shares an interesting view about human mind’s ability to instinctively solve math problems. It shows how the mind is wired to perform some seemingly complex math tasks with ease.

To quote it from the article “Whenever we choose a shorter grocery line over a longer one, or a bustling restaurant over an unpopular one, we rally our approximate number system, an ancient and intuitive sense that we are born with and that we share with many other animals. Rats, pigeons, monkeys, babies — all can tell more from fewer, abundant from stingy. An approximate number sense is essential to brute survival: how else can a bird find the best patch of berries, or two baboons know better than to pick a fight with a gang of six?” It’s interesting to know that not only the human brain works this way but even baboons’ and rodents’ work in the same manner.

In fact, research has shown that new born babies if found to be good at deciphering approximations with ease, will carry on the same trait when they grow up and have to deal with abstruse mathematical problems. NYT states: “One research team has found that how readily people rally their approximate number sense is linked over time to success in even the most advanced and abstruse mathematics courses. Other scientists have shown that preschool children are remarkably good at approximating the impact of adding to or subtracting from large groups of items but are poor at translating the approximate into the specific.” In fact, it goes further and suggests that Math teachers should emphasize on the power of approximation early on in the child’s education so he can hone this natural skills to an advantage. To quote “Taken together, the new research suggests that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.”

At LazyMaths.com, we precisely try to encourage our students to leverage these skills of approximation. We have found that with practice, the line between approximation and precision can be diluted if not fully erased. In the section of Don’t Solve, LazyMaths offers a large number of examples of a variety of Math problems attempted using the techniques of approximation.

If you are interested in checking out how good your natural approximation skills are, here’s a quick test.
http://www.nytimes.com/interactive/2008/09/15/science/20080915_NUMBER_SENSE_GRAPHIC.html