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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><marquee><font color="Green"><h1>APTITUDE</h1></center></strong></font></TR></marquee><TR><TD align="left" width="200" valign="top"><table><TR><a href="numbers.html"><strong>Numbers</strong></a></TR><br><TR><a href="hcf.html"><strong>H.C.F and L.C.M</strong></a></TR><br><TR><a href="dec.html" ><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html" ><strong>Square and Cube roots</strong></a></TR><br><TR><a href="average.html" ><strong>Average</strong></a></TR><br><TR><a href="pnumbers.html" ><strong>Problems on Numbers</strong></a></TR><br><TR><a href="problemsonages.html"><strong>Problems on Ages</strong></a></TR><br><TR><a href="surdsandindices.html"><strong>Surds and Indices</strong></a></TR><br><TR><a href="percent.html" ><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html" ><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html" ><strong>Ratio And Proportions</strong></a></TR><br><TR><a href="partnership.html"><strong>Partnership</strong></a></TR><br><TR><a href="chainrule1.html"><strong>Chain Rule</strong></a></TR><br><TR><a href="timeandwork.html" ><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html" ><strong>Pipes and Cisterns</strong></a></TR><br><TR><a href="timeanddistance.html"><strong>Time and Distance</strong></a></TR><br><TR><a href="trains.html" ><strong>Trains</strong></a></TR><br><TR><a href="boats.html"><strong>Boats and Streams</strong></a></TR><br><TR><a href="alligation.html"><strong>Alligation or Mixture </strong></a></TR><br><TR><a href="simple.html" ><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html" ><strong>Areas</strong></a></TR><br><TR><a href="volume.html"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html" ><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html" ><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html" ><strong>Clocks</strong></a></TR><br><TR><a href="" ><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html" ><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html" ><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html"><strong>Oddmanout and Series</strong></a></TR><br><TR><a href=""><strong>Data Interpretation</strong></a></TR><br><TR><a href="probability.html"><strong>probability</strong></a></TR><br><TR><a href="percom1.html" ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html" ><strong>Puzzles</strong></a></TR></table></TD><TD valign="top"><a href="pnumbers.html" name="right"><b>BACK</b></a><font size="5"><center><b>PROBLEMS ON NUMBERS</b></center></font><br><br> <font size="5"><b>SOLVED PROBLEMS</b></font><br><br><br><br> <font size="4"> <b>Simple problems</b>:<br><br>1.What least number must be added to 3000 to obtain a number<br> exactly divisible by 19?<br>Solution:<br>On dividing 3000 by 19 we get 17 as remainder<br>Therefore number to be added = 19-17=2.<br><br>2.Find the unit's digit n the product 2467 153 * 34172?<br>Solution: <br> Unit's digit in the given product=Unit's digit in 7 153 * 172<br>Now 7 4 gives unit digit 1<br>7 152 gives unit digit 1<br>7 153 gives 1*7=7.Also 172 gives 1<br>Hence unit's digit in the product =7*1=7.<br><br>3.Find the total number of prime factors in 411 *7 5 *112 ?<br>Solution:<br><br> 411 7 5 112= (2*2) 11 *7 5 *112<br> = 222 *7 5 *112<br><br>Total number of prime factors=22+5+2=29<br><br> 4.The least umber of five digits which is exactly<br> divisible by 12,15 and 18 is?<br>a.10010 b.10015 c.10020 d.10080<br>Solution:<br>Least number of five digits is 10000<br>L.C.Mof 12,15,18 s 180.<br>On dividing 10000 by 180,the remainder is 100.<br>Therefore required number=10000+(180-100)<br> =10080.<br><br>Ans (d).<br><br>5.The least number which is perfect square and is divisible<br> by each of the numbers 16,20 and 24 is?<br><br>a.1600 b.3600 c.6400 d.14400<br>Solution:<br>The least number divisible by 16,20,24 = L.C.M of 16,20,24=240<br> =2*2*2*2*3*5<br><br>To make it a perfect square it must be multiplied by 3*5.<br>Therefore required number =240*3*5=3600.<br>Ans (b).<br><br>6.A positive number which when added to 1000 gives a sum ,<br>which is greater than when it is multiplied by 1000.<br>The positive integer is?<br><br>a.1 b.3 c.5 d.7<br><br>Solution:<br><br>1000+N>1000N<br> clearly N=1. <br><br>7.How many numbers between 11 and 90 are divisible by 7?<br>Solution:<br>The required numbers are 14,21,28,...........,84.<br>This is an A.P with a=14,d=7.<br>Let it contain n terms <br><br>then T =84=a+(n-1)d<br> =14+(n-1)7<br> =7+7n<br> 7n=77 =>n=11.<br><br>8.Find the sum of all odd numbers up to 100?<br>Solution:<br>The given numbers are 1,3,5.........99.<br>This is an A.P with a=1,d=2.<br>Let it contain n terms 1+(n-1)2=99<br> =>n=50<br>Then required sum =n/2(first term +last term)<br> =50/2(1+99)=2500.<br><br>9.How many terms are there in 2,4,6,8..........,1024?<br>Solution:<br>Clearly 2,4,6........1024 form a G.P with a=2,r=2<br>Let the number of terms be n<br><br>then 2*2 n-1=1024<br> 2n-1 =512=29<br> n-1=9 <br> n=10.<br><br>10.2+22+23+24+25..........+28=?<br>Solution:<br>Given series is a G.P with a=2,r=2 and n=8.<br>Sum Sn=a(1-r n)/1-r=Sn=2(1-28)/1-2.<br> =2*255=510.<br><br>11.Find the number of zeros in 27!?<br>Solution:<br>Short cut method :<br> number of zeros in 27!=27/5 + 27/25<br> =5+1=6zeros. <br><br><a href="pnumbers.html" name="right"><b>BACK</b></a><br><br></font></TD></TR></table></html>?? 快捷鍵說明
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