Q.16- which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21, 33 and 54?
a) 9123 b) 9383 c) 8727 d) none of these
i dint get the method used in the book to solve this question. can we come up with an alternative?
Hook or crook method would be the best one here bro,
as we can directly check with options and can come to the conclusion that option b satisfies it completely......
or in case u need a method then it will like this lets say number is a then we have (a+7249) is divisible by 12, 14, 21, 33 and 54 that means divisible by 2,3,7,11 so the end digit would be a odd number as odd+odd = even hence and a should give remainder of 2 when divided by 3 as 7249 leaves remainder as 1 .... going by this way we can reach the solution that will be tedious and cumbersome .. i will prefer the upper one .....
Q.16- which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21, 33 and 54?
a) 9123 b) 9383 c) 8727 d) none of these
i dint get the method used in the book to solve this question. can we come up with an alternative?
In this case you are lucky that there's only one that fulfills the conditions. ie b) option a and c yield numbers that are not divisible by 11 so maybe if you'd tested that first you'd reach the answer quicker. but that's not a good method. what was suggested above ie using remainders seems fine.
Q.16- which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21, 33 and 54?
a) 9123 b) 9383 c) 8727 d) none of these
i dint get the method used in the book to solve this question. can we come up with an alternative?
do it by options...and check divisibility of 7 for 2nd option...u will get ur ans
Don't insist on using something just for its sake when you don't follow the logic. use the method u r using.. but just for your info by alligation you would do it like: water:alcohol 10:90(1:9) to 12.5:87.5(1:7) difference in water=1/7-1/9=2/63 so water you would add=2/63*90=2.85 i think..somewhere there.
btw this is a very strong drink you are making!!! lol generally its alcohol thats 12.5% by volume in drinks. check your heineken can. there you go some general knowledge for you too!! who knows- might help in your interview. :p
NO Yaar i dont think......this will do....after addition of water the total concentration turns to 12.5% and the volume of soln....is not 90 but 90+ (additional water added) x....Say the volume of mixture initially is 90 l.....
So it wud be 9+x/90+x =1/8.....Therefore x= 2.5X...something of dat sort...am I RITE???? Thats Ok...i was trying to solve the Qs in alligation method as it was dere in chapter of alligations??? "Cos...i saw i cud save a lot of time in the method of alligations....?? Dats why... Ny One dere Do help???
do it by options...and check divisibility of 7 for 2nd option...u will get ur ans
Hi ya u can solve thru options fine......... But this is how its actually solved it Lcm of 12,14,21,33,54 is 8316,,,k...... So now we are asked to add largest 4 digit no so that the result is also divisible by these nos..... Hmmm...8316.... is divisible by this no.... 7249...is 1067 short of 8316.... So the number to be added...to satisfy the conditions is...... 8316+ 1067==== 9383... Ans....
These are some questions on percentages and P&L; in which i've got doubt:
Q1. Suppose that 25% of all the wise people are nice and half of all the nice people are wise. Suppose further that 25% of all the people are neither wise nor nice. What percent of all the people are both wise and nice? a. 10% b. 15% c. 20% d. 25% e. 30%
Q2. A merchant uses fake weight while selling and ends up making a profit of 20%, though he claims to sell at cost price. One day he swaps his scale by mistake and therefore ends up making a loss. How much loss did he make? a. 20% b. 16.67% c. 14.28% d. 25% e. 12.5%
3. In n election, only 2 candidates contested...20% voters didnt vote, 120 votes were declared invalid...winner got 200 more votes than opponent and thus 41% of votes in the voterlist. Find... 1. total votes casted 2. total no. of voters 3. no. of valid votes
Q4. 2/5 of the voters promise to vote P and the rest promised to vote Q. Of these, on the last day 15% of the voter went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q, and p lost by 2 votes. Then, the total number of voters is :
5. In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carriers 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in-group A together carry at least 60% of the total marks. (CAT 2004) Q2. If group B contains 23 questions, then how many questions are there in group C? a. 1 b. 2 c. 3 d. Cannot be determined
Q6. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What percent of the total amount paid by me was paid for the pens?
Q7. The number of votes not cast for the Praja Party increased by 25% in the national general election over those not cast for it in the previous Assembly polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the Praja Party in the previous Assembly Polls?
Q8. A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?
@nimisha Here are my answers, 1)20% 2)16.67% 3)total votes casted-3200 Total voters-4000 Total no. of valid votes-3080 4)total no. of voters is 100. P=49,Q=51 5)1 question in group c 6)62.5% 7)140,000 voted for praja party last year 35 m.
NO Yaar i dont think......this will do....after addition of water the total concentration turns to 12.5% and the volume of soln....is not 90 but 90+ (additional water added) x....Say the volume of mixture initially is 90 l.....
So it wud be 9+x/90+x =1/8.....Therefore x= 2.5X...something of dat sort...am I RITE???? Thats Ok...i was trying to solve the Qs in alligation method as it was dere in chapter of alligations??? "Cos...i saw i cud save a lot of time in the method of alligations....?? Dats why... Ny One dere Do help???
haha.. you took 9+x/90+x and I took 10+x/100+x x's value will keep changing if you took different values.. so there's one missing information in this question. the answer can indeed be 2.5 if initial vol was 90, if initial vol was 100 ans is 2.85 and so on.. You can't just say how much volume of water to change its concentration from 10 to 12.5% you have to say "in how much volume" ie total volume initially to solve uniquely. cos for that matter i can take 13/130 initially that will give me a different answer. as for the method what I told was the alligation method, not equations. Alligation - Wikipedia, the free encyclopedia check here.
Q1. If 2 Q2. Find the 28383rd digit of 123456789101112.......
Q3. what is the remainder when (1!)^3 + (2!)^3......(1152!)^3 is divided by 1152?
Q4. If you form a subset of integers chosen from between 1 to 3000, such that no two integers add to amultiple of nine, what can be the maximum number of elements in the set?
Q5. What are the last 2 digits of (201*202*203*204*246*247*248*249)^2?
Q6. what is the remainder when 2(8!)-21(6!) divides 14(7!)+14(13)!?
@shashank 1st ans is not right..its 15% plz do explain the method for others..
esp in last question, i think i'm making a silly mistake.. i'm doing it as ratio of distance(A:B) is 1.25:1 difference is 7 . so .25D is 7 so D is 28. what is the mistake i'm making??
@shashank 1st ans is not right..its 15% plz do explain the method for others..
esp in last question, i think i'm making a silly mistake.. i'm doing it as ratio of distance(A:B) is 1.25:1 difference is 7 . so .25D is 7 so D is 28. what is the mistake i'm making??
Hi, Regarding the first answer i made a silly mistake. I didnt consider the 25% who are neither wise nor nice. Correct answer is 15%.
For the last one, Lets consider distance travelled by A as x. So distance travelled by B in the same period is (x-7). Both of them take the same time. So, x/(x-7)=Sa/Sb. But,Sa/Sb=5/4. On solving,we get,x=35m,which is the distance of the race. You are taking the ratio of distances. It should be speed.
I am in train currently on mobile and will be posting remaining answers soon :-)
2)suppose the merchant has bought 1200gm for 1000rs. So to make 20% profit he sells 1000gm for 1000rs. Now if scales are exchanged he gives 1200gm for 1000rs. Thats a loss of 16.67%. I have used 1200 just to bring into effect the 20%. I would advise you to do the same rather than using variables.
3)let total voters be T. Let winner get x votes.Therefore T/5 didnt vote,120 invalid. Loser got x-200 votes. And x=41T/100. So, T=120+T/5+x+x-200. Put x=41T/100. 2T=8000 T=4000. Total votes casted are:4000-800=3200. Number of valid votes are:3200-120=3080
4)let there be T voters. So P has been promised of 2T/5 votes and Q of 3T/5 votes. Now,15% of 2T/5 votes went in favour of Q and 25% of 3T/5 votes went in favour of P. On adding and subtracting from the respective parties, we get 2 answers as P=49T/100 and Q=51T/100. But, Q-P=2. On solving, T=100.
5)i did this by the trial and error method. If we substitute C=1,we get A=76 and A/total as 76/125, which is just above 60% and hence satisfies the condition. If we try C=2,we get A=75 and A/total as 75/127,which is below 60%. So the answer is C=1.
6)let cost of each pen=x, Cost of each pencil=y, Cost of each eraser=z. Now i bought materials worth, 5x+7y+4z.....(1) Rajan bought materials worth, 6x+14y+8z.....(2) Now by second condition, 3(5x+7y+4z)=2(6x+14y+8z). On simplification, 3x-7y-4z=0. Just by the look of it you can see that,the equation is satisfied by x=5,y=1,z=2. Hence from (1), i paid 40Rs.
7) let votes for the praja party last year be x1, let votes not for them be y1. Let votes for praja party this year be x2,let votes not for them be y2. Hence, x1+y1=260000 x2+y2=260000 Also, y2=5(y1)/4. Now, 2(x1-y1)=(y2-x2)....remember they lost this year and had won last year. Now,bring the equation in terms of y1 and solve. We get y1=120000 x1=140000
8]i have explained that in my previous post. Phew. What a post!!! What r u doing currently nimisha? Are you with one of the dream teams? You are most welcome to the INDIA UNITED DREAM TEAM. We need enthusiastic people like you there. Keep posting. Cheers, Shashank.
Q1. If 2 Q2. Find the 28383rd digit of 123456789101112.......
Q3. what is the remainder when (1!)^3 + (2!)^3......(1152!)^3 is divided by 1152?
Q4. If you form a subset of integers chosen from between 1 to 3000, such that no two integers add to amultiple of nine, what can be the maximum number of elements in the set?
Q5. What are the last 2 digits of (201*202*203*204*246*247*248*249)^2?
Q6. what is the remainder when 2(8!)-21(6!) divides 14(7!)+14(13)!?
I tried to solve a few of dem....Hope it works....1. its 4+3/4-3== 7...2.28383 digit ....k....1-9=== 9 digits....10-99== 90*2 =180 digits...100-999 === 900*3 =2700 digits...1000-9999 =9000*4 =36000 digits...total of above is 2889 digits....so it lies in between 1000-9999...now rest are 28383 - 2889 = 25494..digits...so 25494/4 ==6373.5...so no is 7372.5 so its 7373..0.5 means 2nd digit...so its 3....ans....
Q1. If 2 Q2. Find the 28383rd digit of 123456789101112.......
Q3. what is the remainder when (1!)^3 + (2!)^3......(1152!)^3 is divided by 1152?
Q4. If you form a subset of integers chosen from between 1 to 3000, such that no two integers add to amultiple of nine, what can be the maximum number of elements in the set?
Q5. What are the last 2 digits of (201*202*203*204*246*247*248*249)^2?
Q6. what is the remainder when 2(8!)-21(6!) divides 14(7!)+14(13)!?
Ans to Q.51the eqn can be simplified to {14(7!)+ 14!}/13(7!)and the remainder in discase is 1.....
Q1. If 2 Q2. Find the 28383rd digit of 123456789101112.......
Q3. what is the remainder when (1!)^3 + (2!)^3......(1152!)^3 is divided by 1152?
Q4. If you form a subset of integers chosen from between 1 to 3000, such that no two integers add to amultiple of nine, what can be the maximum number of elements in the set?
Q5. What are the last 2 digits of (201*202*203*204*246*247*248*249)^2?
Q6. what is the remainder when 2(8!)-21(6!) divides 14(7!)+14(13)!?
Q 3.....1152 is 2^9 * 3 ^2...so now wat we can do is find wich has the follwing factors.....and dose will give 0 remainder......the Qs will get reduced...ill solve n let u knw....Im in office so didnt solve....it..will do so....ASAP
Q1. If 2 Q2. Find the 28383rd digit of 123456789101112.......
Q3. what is the remainder when (1!)^3 + (2!)^3......(1152!)^3 is divided by 1152?
Q4. If you form a subset of integers chosen from between 1 to 3000, such that no two integers add to amultiple of nine, what can be the maximum number of elements in the set?
Q5. What are the last 2 digits of (201*202*203*204*246*247*248*249)^2?
Q6. what is the remainder when 2(8!)-21(6!) divides 14(7!)+14(13)!?
My take 1) -7 2)the digit is 3. 3)225 4)i think it has to be 1335 5)76. Very easy. 6)i think its 1.