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.
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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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.
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.
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.
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
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?
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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.
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.
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.
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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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.
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.
A lot of mathematics exams nowadays, e.g. GMAT, SAT, etc, are either completely multiple choice or they have multiple-choice components. These exams required students to solve a stipulated large number of questions within a small amount of time. Students break a lot of sweat over solving these questions, by trying to solve them completely like other questions, and not utilizing the information that is in front of them.
One of the basic difference between multiple-choice questions and other questions is that for multiple-choice ones you have to just figure out the answer, and for achieving this objective, you need not necessarily solve the question completely, as the answer is right in front of you, among the 4-5 choices that have been provided.
Ball-park, or possible range strategy, is one such very effective method to quickly solve a multiple-choice question in arithmetic. In order to use it, you first make a quick guess of what the possible range of your answer will be. Once, you have made such a guess, you can easily eliminate all the other answers, which don’t fall in that range, and so can be ruled out as a choice for the possible answer. You are now left with just 1 or 2 choices, which you can just plug-in to confirm which one is the correct answer.
This strategy doesn’t work well if all the choices are in the possible range, and it is particularly useful when the answers are scattered over a large range, as in the following example:
If 0.303z = 2,727, then z =
a) 9,000
b) 900
c) 90
d) 9
e) 0.9
We can notice that the range of answers is too large, so we can use ball parking to solve this question. .303 is very close to 1/3, which means 1/3 of z = 2,727, then what answer could be possibly correct. You don’t even have to do the math. 2,727 is about 1/3 of 9,000; therefore, the answer must be 9,000, according to the Ballpark Strategy (note that there are no other answers even in the 9,000 range.
If you don’t use the ballpark strategy, you could multiply both sides by 1000 to eliminate the decimal points, and then divide 2,727,000 by 303 and get the same answer, although after spending much more time.
Another important use of this strategy is to double-check your answer. Once you have solved a multiple-choice arithmetic question, you should confirm whether the answer lies in the ballpark of what the answer could be.
So, invest sometime in learning and practicing to use ball-parking. This will allow you to solve the arithmetic questions much faster and will save you precious time, enabling you to score much higher.
LazyMaths.com focuses on this strategy and has hundreds of examples to show how and where one can use ballparking. Visit the Don’t Solve section of the site to know more about it and check out some free examples.
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Our students have reported getting 100% marks in their Math tests using our shortcuts and techniques!
.
(
) = 12
= 1
3m + 6w = 1/4
and w = 
47. Thus option ‘e’ is eliminated as sum of 10 + 20 + 18 = 48.
means 
; find the value of 3.124*1.39.
