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### Clock

1. 1. 1. An accurate clock shows 8 oclock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 oclock in the afternoon? A. 144º B. 150º C. 168º D. 180º View Answer Workspace Report Discuss in Forum2. The reflex angle between the hands of a clock at 10.25 is: 1º A. 180º B. 192 2 1º C. 195º D. 197 2 View Answer Workspace Report Discuss in Forum3. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through: A. 145º B. 150º C. 155º D. 160º View Answer Workspace Report Discuss in Forum4. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 oclock, the true time is: 7 A. 59 min. past 3 B. 4 p.m. 12 7 3 C. 58 min. past 3 D. 2 min. past 4 11 11 View Answer Workspace Report Discuss in Forum5. How much does a watch lose per day, if its hands coincide every 64 minutes? 8 5 A. 32 min. B. 36 min. 11 11 C. 90 min. D. 96 min.6. At what time between 7 and 8 oclock will the hands of a clock be in the same straight line but, not together? 2 A. 5 min. past 7 B. 5 min. past 7 11 3 5 C. 5 min. past 7 D. 5 min. past 7 11 11 View Answer Workspace Report Discuss in Forum7. At what time between 5.30 and 6 will the hands of a clock be at right angles? 5 7 A. 43 min. past 5 B. 43 min. past 5 11 11 C. 40 min. past 5 D. 45 min. past 5 View Answer Workspace Report Discuss in Forum
2. 2. 8. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: A. 0º B. 10º C. 5º D. 20º View Answer Workspace Report Discuss in Forum9. At what angle the hands of a clock are inclined at 15 minutes past 5? 1º A. 58 B. 64º 2 1º 1º C. 67 D. 72 2 2 View Answer Workspace Report Discuss in Forum10. At 3.40, the hour hand and the minute hand of a clock form an angle of: A. 120º B. 125º C. 130º D. 135º11. How many times are the hands of a clock at right angle in a day? A. 22 B. 24 C. 44 D. 48 View Answer Workspace Report Discuss in Forum12. The angle between the minute hand and the hour hand of a clock when the time is 8.30, is: A. 80º B. 75º C. 60º D. 105º View Answer Workspace Report Discuss in Forum13. How many times in a day, are the hands of a clock in straight line but opposite in direction? A. 20 B. 22 C. 24 D. 48 View Answer Workspace Report Discuss in Forum14. At what time between 4 and 5 oclock will the hands of a watch point in opposite directions? A. 45 min. past 4 B. 40 min. past 4 4 6 C. 50 min. past 4 D. 54 min. past 4 11 11 View Answer Workspace Report Discuss in Forum15. At what time between 9 and 10 oclock will the hands of a watch be together? A. 45 min. past 9 B. 50 min. past 9
3. 3. 1 2 C. 49 min. past 9 D. 48 min. past 9 11 1116. At what time, in minutes, between 3 oclock and 4 oclock, both the needles will coincide each other? 1" 4" A. 5 B. 12 11 11 4" 4" C. 13 D. 16 11 11 View Answer Workspace Report Discuss in Forum17. How many times do the hands of a clock coincide in a day? A. 20 B. 21 C. 22 D. 24 View Answer Workspace Report Discuss in Forum18. How many times in a day, the hands of a clock are straight? A. 22 B. 24 C. 44 D. 48 View Answer Workspace Report Discuss in Forum19. A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct? A. 2 p.m. on Tuesday B. 2 p.m. on Wednesday C. 3 p.m. on Thursday D. 1 p.m. on Friday View Answer Workspace Report Discuss in Forum
4. 4. Problem SolvingClock AnglesCategories : Problem SolvingClock based math problems are among the most challenging and interesting problems tocrack.BasicsFor every 60 units that a minute hand move in an hour , the hour hand moves 5 units.For 12 hours the hour hand completes 360 degrees1 hour = 360/12 = 30 degrees60 minutes = 30 degreesDegrees turned by hour hand in 1 minute = 0.5 degreesFor 1 hour the minute hand completes 360 degrees1 hour = 360 degrees60 minutes = 360 degreesDegrees turned by minute hand in 1 minute = 6 degrees<!--break-->Lets test what we have learned:Q) Find the degree between hour hand and minute hand at 3:32Hour hand = 31 minute ( hour hand) = 0.5 degrees3 hours = 3*0.5*60(1 hour= 60 minutes)3 hours ( 3o clock) = 90 degreesMinute Hand = 32...Learn moreGMAT Weighted Average - Tutorial and QuestionsCategories : Problem Solving
5. 5. Average Question is an important topic in GMAT problem solving and data sufficiency. Let usstart with the Basics.Average (Arithmetic Mean)Average of n numbers a1, a2, a3, a4, a5....an(An) = (a1+a2+.....an) /nExample: Find the average of 34, 56, 75 and 83Answera1 = 34a2= 56a3=75a4 = 83Total Number of Elements (n) = 4Average (An) = (a1+a2+a3+a4)/n= (34 + 56 + 75 + 83)/4 = 62Shortcut to Remember: An x n = a1+a2+.......anLet us straight away apply this shortcutQ) The average of four numbers is 20. If one of the numbers is removed, the average of theremaining numbers is 15. What number was removed?(A) 10(B) 15(C) 30(D) 35(E) 45Answer:Four Numbers = a1, a2, a3, a4n=4An = 20An x n = a1 + a2 + a3 + a420 x 4 = a1 + a2 + a3 + a4 -> Statement 1Let us assume that a4 has been removedn=315 x 3 = a1 + a2 + a3...Learn moreTop 10 GMAT Problem Solving Tips
6. 6. Categories : GMAT Tips, Problem SolvingThe Problem Solving (PS) section of the GMAT may not be as quirky as the Data Sufficiencysection of the test – but that doesn‘t mean you don‘t need to study for it! PS questions requiremore ―straight math‖ than Data Sufficiency questions; in other words, they‘ll probably be morelike the questions you‘re used to seeing on high school and college math tests. The best way tostudy? Master the basic concepts from geometry, algebra, statistics, and arithmetic — thencheck out these 10 helpful tips!1. Make sure your fundamentals are strong.The GMAT doesn‘t allow you to use a calculator—which means you need to be quick andaccurate with basic calculations. Be able to multiply and divide decimals. Know common higherpowers and roots. Have fractions down to a science: Knowing right away whether 3/8 is lessthan 5/12 will mean you have more time later to work on more complicated calculations.2. Choose numbers wisely.Even questions that don‘t contain variables can still be tackled by choosing numbers wisely.For example, if a question asks you about ―a multiple of 6,‖ it‘s probably quicker to work with aparticular multiple of 6 (say, 12) than the abstract ―multiple of 6.‖ While studying, identify thekind of problems where this strategy can be applied....Learn moreHow to solve work and rates problem in GMATCategories : Data Sufficiency, Problem Solving, Rate Problems, Work ProblemsCarefully go through the following question types. These are the standard work rate problemsthat you would encounter in your GMAT Exam.Working TogetherIn questions where individuals work at different speeds, we typically need to add theirseparate rates together. Make sure you keep your units straight. This doesn‘t mean wastingtime and writing each and every one out, but rather simply recognizing their existence. Notethat when working together, the total time to complete the same task will be less than BOTHof the individual rates, but not necessarily in proportion. Nor, are you averaging or adding thegiven times taken. You must add rates.Q) A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7hours. If both workers load one truck simultaneously while maintaining their constant rates,approximately how long, in hours, will it take them to fill 1 truck?A. 0.15
7. 7. B. 0.31C. 2.47D. 3.23E. 3.25The rate of worker #1 is 1 truck/6 hours. This can also be 1/6 trucks/1 hour. The rate ofworker #2 is 1/7. When together, they will complete 1/6 + 1/7 trucks/ 1 hour.1/6 + 1/7 = 6/42 + 7/42 = 13/42 trucks/1 hour. Remember the question is asking for thenumber of hours to fill 1 truck, NOT the number of...Learn moreGMAT Simple Interest and Compound InterestCategories : Data Sufficiency, Interest Problems, Problem SolvingSimple interest and compound interest - essential topics for an MBA. GMAC thinks the sametoo. So you will find these questions randomly distributed in your GMAT Exam.Simple interest is the most basic and is a function of P, the principle amount of moneyinvested, the interest rate earned on the principle, i, and the amount of time the money isinvested, t (this is usually stated in periods, such as years or months).The resulting equation is:Interest = iPtIn basic terms, the above equation tells us the amount of interest that would be earned on aprinciple amount invested (P), for a given time (t) at a given interest rate (i).ExampleIf you invested \$1,000 (P = your principle) for one year (t = one year) at 6% simple interest (i= given interest rate), you would get \$60 in interest at the end of the year and would have atotal of \$1,060.For compound interest, you would earn slightly more. Let‘s look at similar type problem,though this one involves compound interest.Q) Mr. Riley deposits \$500 into an account that pays 10% interest, compounded semiannually.How much money will be in Mr. Riley‘s account at the end...Learn moreUsing Venn Diagrams to solve GMAT Set Questions
8. 8. Categories : Data Sufficiency, Venn Diagrams, Problem Solving, SetsOn your GMAT, you will encounter 1-3 questions that contain overlapping groups with specificcharacteristics. You will almost never see more than two characteristics (since you can‘t draw3D on your scratch paper). For illustration, let‘s take a look at the following Data Sufficiencyexample:Q) Of the 70 children who visited a certain doctor last week, how many had neither acold nor a cough?(1) 40 of the 70 children had a cold but not a cough.(2) 20 of the 70 children had both a cold and a cough.There are two characteristics (cough and cold) and two categories for each (yes and no), sothere are four total categories, as indicated by this matrix:I‘ve filled in the given information from both statements, and the parenthetical information isinferred. This clearly lays out the 4 combinations of options. If we sum vertically, we can inferthat there are 60 total children with colds. Because there are 70 total children, this also meansthat 10 do NOT have colds. The bottom-right quadrant cannot be found because we do notknow how those 10 children get divided between the two empty boxes. Choice E – together thestatements are insufficient...Learn moreNever actually understood Absolute Values ? Here is your chance!Categories : Absolute Value, Data Sufficiency, Problem SolvingAbsolute Values (AVs) questions in GMAT can be a time saver for you if you understand afew rules. Capture the following notes and use it as a reference for your GMAT exam.1. Absolute Value equations are two equations disguised as oneYou can split up any equation involving absolutes into two, and solve for each solution. Onewill look identical to the given, and the other is found by multiplying the inside by -1.
9. 9. Remember to multiply the entire expression by -1.| (x + 5)/3 | = 11 turns into:(x + 5)/3 = 11, and(x+5)/3 = -11x + 5 = 33x + 5 = -33x = 28 x = -38Note that plugging either x = 28 or x = -38 into the original equation will check out. Also notethat solutions for variables within absolute value questions can be negative. What is spit out ofthe AV cannot be negative, but what goes in can be anything.2. Think of Absolute Values as distances from zeroIf an AV = 15, that means whatever is inside the AV is exactly 15 above or below zero on thenumber line.| x + 5 | = 15_____-20_____-15_____-10__________0__________+10_____+15_____+20_____x = -20 and x = 10. Note that this is a SHIFT of -5 from the constant on the...Learn moreGMAT Fractions - Dont get lost in the calculationsCategories : Data Sufficiency, Fractions, Problem SolvingHave you wondered how writers can make a seemingly simple GMAT topic like fractions intotime-consuming calculations. One strategy that GMAT test takers must adopt to simplify thecalculations. For exampleDividing by 5 is the same as multiplying by 2/10. For example:• 840/5 = ?• 840/5 = 840*(2/10) = 84*2 = 168Multiplying or dividing by 10‘s and 2‘s is generally easier than using 5‘s. 90% of the time,fractions will be easier to perform arithmetic. Decimals are sometimes more useful whencomparing numbers relative to one another, such as in a number line, but these questions arethe exception. Even if given a decimal (or percent) looks easy, quickly convert to afraction. Some common ones to memorize:• 1/9 = 0.111 repeating• 1/8 = 0.125• 1/7 = ~0.14
10. 10. • 1/6 = 0.166 repeating• 1/5 = 0.20• 1/4 = 0.25• 1/3 = 0.333 repeating• 1/2 = 0.5 repeatingNote: Multiples of these, such as 3/8 (0.375) are also important to remember, but can easilybe derived by multiplying the original fraction (1/8 * 3 = 3/8 = 0.125 * 3 = 0.375)Denominators are super important. A denominator of a reduced fraction with a multiple of7 will not have a finite...Learn moreGMAT Solid Geometry - Rectangular Solids and CylindersCategories : Data Sufficiency, Problem Solving, Rectangular Solids and CylindersRectangular SolidLearn the concepts behind volume and surface area before you start solving GMAT Solidgeometry problems. All solid geometry problems come down to this - length, breadth andheight. For data sufficiency questions, look out for values of l, b and h. if any of them aremissing then it would be easy to eliminate answer choices.6 rectangular faces constitute a rectangular solidThe formulas you need to remember for a rectangular solid areVolume = Length (l) x Width (w) x Height (h)Surface Area = (2 x Length x Width) + (2 x Length x Height) + (2 xWidth x Height)"If length = width = height, that means that the rectangular solid is, infact, a cube."Terminologies
11. 11. Vertex: Wow! quite a confusing word? Not reallyVertex = Cornera) Vertex is the number of corners in a...Learn moreHow to score well in GMAT Number properties?Categories : Number Properties, Problem SolvingGMAT Number properties may sound scary, but they just constitute elementarymathematical principles. You probably know most of these principles by memory; if not, youcould easily execute a calculation to ascertain them. The best option, though, is to study theseprinciples enough that they seem intuitive. The GMAT Quantitative section is all about savingtime; making number theory second nature will definitely save you some valuable seconds.1.Odds and EvensAdditionEven + even = even (12+14=36)Odd+ Odd = even (13+19=32)Even + Odd = odd (8 + 11 = 19)To more easily remember these, just think that a sum is only odd if you add an even and anodd.MultiplicationEven x even = even (6 x 4 = 24)Odd x odd = odd (5 x 3 = 15)Even x odd = even (6 x 5= 30)To more easily remember these, just think that a product is only odd if you multiply two odds.Example QuestionIf r is even and t is odd, which of the following is odd?A. rtB. 5rtC. 6(r^2)tD. 5r + 6tE. 6r + 5tIn this example, we could either plug in numbers for r and t, or we could use our knowledge ofnumber theory to figure out the...Learn more
12. 12. Solving GMAT Questions with two linear equations and two unknownsCategories : Equations, Problem SolvingIn order to solve such equations, you need at least 2 distinct equations involving theseunknowns.For example, if we are trying to solve for x and y, we wont be able to solve it using these 2equations.2x + y = 144x + y - 14 = 14 - yWhy? Because the two equations on top are the same. If you simplify the second equation,you get 4x + 2y = 28 which reduces to 2x + y = 14 - the same equation as the first. If thetwo equations are the same, then there will be infinitely many values for x and y that willsatisfy the equations. For example, x = 2 and y = 10 satisfies the equation. So does x = 4and y = 8. And so does x = 6 and y = 2.In order to solve for an actual value of x and y, we need 2 distinct equations.For example, if we had2x + y = 14 --------(1)x - y = 4 ----------(2)Then from equation (2), we can get x = 4 + y and substitute that into equation (1) to get:2(4 + y) + y = 14 We can then solve for y. See if you got y = 2 Once youve got y = 2, youcan substitute that into x= 4 + y to get x = 6.An important lesson here is that you need as many distinct equations...Learn moreGMAT Word Problems - BasicsCategories : Word Problems, Problem SolvingWord problems on the GMAT get an unfair reputation for being especially challenging.However, it‘s helpful to think of them as just dressed-up algebra. The real challenge is thatthey are (1) long, (2) boring, and (3) require translation from ‗English‘ to ‗Math.‘ Here are afew questions to ask yourself to make sure you fully break down and understand the problemBEFORE you start to solve!What is the problem really asking? Make sure to understand what the answer choices represent. Are they the total number ofdollars of profit? The profit accumulated by Jenny only? The percent increase in profit from
13. 13. June to July? Taking the time to do this will also ensure you never leave a problem halffinished. If you dive into setting up an equation too quickly, you may realize half-way throughthat you‘re solving for the wrong variable. Sometimes word problems will add an extra step atthe end. You may be busy solving for ―x‖ and forget that the problem is asking for the value of―1/x‖.What information am I given? The best thing about word problems is that they offer information is an organized manner.Go sentence by sentence, translating any ‗English‘ into ‗Math,‘ looking for the relationship...Learn moreStatisticsCategories : Data Sufficiency, Mean, Median, Mode, Standard Deviation, Descriptive Statistics,ProblemSolvingEven if you fear statistics by its reputation, it is one of the easiest sections in the GMATbecause a standard set of questions is asked and anyone who understands the fundamentalsthat I shall describe will be able to ace the questions. The three most basic topics in statsare mean, mode, and median. Usually, the GMAT will go one step further into range andstandard deviation.Mean: Mean is the average. Let‘s say there are two numbers: 6 and 8. The mean would be:(6+8)/2 =14/2 =7. If you analyze the number 7, it makes sense that it is average of 6 and 8.Using the same approach, the mean of n numbers a1,a2,a3…….an would be(a1+a2+a3…..+an)/n. If you remember this formula, you should be able to do well with meanquestions. We shall discuss some of the standard questions in subsequent blogs, but for rightnow, remember the key formula and start doing some mean and average questions fromGrockit games.Mode: Let‘s say that you are given a set of numbers, such as {4,3,7,9,9,11,10}. In order tofind the mode, you have to arrange the numbers in ascending order and find the number whichoccurs the most. For the set in the example, the ascending order is {3,4,7,9,9,10,11} and 9occurs the most (two times) and thus is the mode in this...Learn moreThree Types of GMAT Profit and Loss ProblemsCategories : Data Sufficiency, Problem Solving, Profit and LossYou will encounter the following three types of Profit/Loss problems in the GMAT:
14. 14. Profit/loss as percentage of Cost PriceIn this case you will be given the cost price and sales price, and will be asked to simplycalculate the profit/loss incurred by the seller by entering into the given transaction. This willbe done by dividing the difference between the Sales Price and the Cost Price by the CostPrice. To convert the decimal into a percentage, you will multiply it by 100.Profit Percentage = ((Sales Price - Cost Price)/Cost Price) x 100Selling price = Z x (Cost price)Where Z is any positive number. When Z < 1 we have a loss. When Z = 1 we have neitherprofit nor loss. When Z > 1 we have a profit.Profit or Loss % = (Z - 1) x 100.Selling price = [(Y / 100) + 1]x (Cost price)Where Y is the profit or loss percentage. When Y < 0 we have a loss. When Y = 0 we haveneither profit nor loss. When Y > 0 we have a profit.Profit/loss as percentage of Sales PriceSometimes the problem will be worded differently and will require the test taker to calculate...Learn moreArea , Perimeter and CircumferenceCategories : Data Sufficiency, Geometry Problems, Problem SolvingA sizeable number of GMAT math test questions belong to the Geometry section. Some ofthese questions test a candidate‘s ability to understand 2-Dimensional Geometry by askingthe candidate to calculate the area, perimeter or circumference of a geometrical shape.The following geometrical shapes are most common – Triangles, Quadrilaterals,Rectangles, Rhombuses, Squares, Circles and Trapeziums.Triangles – A triangle represents an enclosed shape made by joining three straight lines. Thearea of a triangle can be calculated as follows:Area = ½*Base Side*Height of the triangleIn this formula, the Base Side can be any side of the triangle. However, depending on the baseside chosen, height of the triangle needs to be ascertained. Height of the triangle is theshortest perpendicular distance from the Base side to the height of the Apex of that triangle.Note that the height of a triangle may need to be calculated outside the triangle, depending onthe base side chosen.
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