Let N be the smallest positive number such that N^3 ends in 888. Find the sum of digits of N.OPTIONS1) 12 2) 17 3) 8 4) 19 5) None of these Does any one has got his/her hands on PDF unlocker software ?
This was discussed earlier in the thread sometime ago
I remember the answer as 192..it involved using a very long and tedious method
TF question of the day it was if i remember correctly
Please tag me when someone posts a simpler method to do the sum..thanks
Unit digit has to be 2say, a2 is the number(10a + 2)^3 = ...8881000a^3 + 600a^2 + 120a = ....880100a^3 + 60a^2 + 12a = ....88Unit digit of 2a is 8=> Unit digit of a is 4 or 9When unit digit of a is 4b42(100b + 42)^3 = ...888Unit digit of 3*42*42*b + 740 is 8Unit digit of 3*42*42*b is 8Unit digit of b is 4 or 9When unit digit of a is 9b92(100b + 92)^3 = ...888Unit digit of 3*92*92*b + 7786 is 8Unit digit of 3*92*92*b is 2Unit digit of b is 1 or 6So, least number will be 192
What you wanna do? Cracking Password protected PDF or wanna edit secured PDF?
yar,there is one pdf in TF website..of last years xat..I want to just copy Qs from it..currnetly it is locked(read only)..I'd one software but dunno it is lost amid lotsa installations 😛 so askin for help..'ll get back dinner..time.
Unit digit has to be 2say, a2 is the number(10a + 2)^3 = ...8881000a^3 + 600a^2 + 120a = ....880100a^3 + 60a^2 + 12a = ....88Unit digit of 2a is 8=> Unit digit of a is 4 or 9When unit digit of a is 4b42(100b + 42)^3 = ...888Unit digit of 3*42*42*b + 740 is 8Unit digit of 3*42*42*b is 8Unit digit of b is 4 or 9When unit digit of a is 9b92(100b + 92)^3 = ...888Unit digit of 3*92*92*b + 7786 is 8Unit digit of 3*92*92*b is 2Unit digit of b is 1 or 6So, least number will be 192
Didn't click that the ten's digit can be 4/9. Got stuck at (100a+b+2)^3 = ...888
668 is correct for sweets questionIsaac attempts all six questions on an Olympiad paper in order. Each question is marked on a scale from 0 to 10. He never scores more in a later question than in any earlier question. How many dierent possible sequences of six marks can he achieve?
hmm exam mein leave karne wala Q lag rha hai yar,there is one pdf in TF website..of last years xat..I want to just copy Qs from it..currnetly it is locked(read only)..I'd one software but dunno it is lost amid lotsa installations so askin for help..'ll get back dinner..time.
There are many softwares available like 2pdf, or simply you can upload secured PDF to google docs, and go to translate and select English, google will extract text and will make a new unsecured PDF.
I used kind of intuitive pattern....hard to explain....let me try anyway.
See, something like 287287 will be divisible by 287 (it will be 287 x 1001) similarly 3434343434 will be 34 x 101010101 and 237823782378 will be 2378 x 100010001. And so on.
So a number with 45 1s, will be divisible by 1, 111, 11111, 111111111 and so on (all numbers with m 1s where m is a factor of 45). Similarly a number with 140 1s, will be divisible by 1, 11, 1111, 11111, 1111111 and so on (all numbers with n 1s where n is a factor of 140). HCF is 5 so 5 1s gives 11111. Sorry if it is confusing - never articulated that thought process in my head :P
There are many softwares available like 2pdf, or simply you can upload secured PDF to google docs, and go to translate and select English, google will extract text and will make a new unsecured PDF.
Carpenter Rajesh has a circular piece of plywood of diameter 30 feet. He has cut out two disks of diameter 20 feet and 10 feet. What is the diameter of the largest disk that can be cut out from the remaining portion of the plywood piece? (2 marks) (1) > 8.00 feet and ≤ 8.20 feet (2) > 8.21 feet and ≤ 8.40 feet (3) > 8.41 feet and ≤ 8.60 feet (4) > 8.61 feet and ≤ 8.80 feet (5) > 8.81 feet and ≤ 9.00 feet
A property dealer bought a rectangular piece of land at 1000/sq. ft. The length of the plot is less than twice its breadth. Due to its size, there were no buyers for the full plot. Hence he decided to sell it in smaller sized pieces as given below. The largest square from one end was sold at 1200/sq. ft. From the remaining rectangle the largest square was sold at 1150/sq. ft. Due to crash in the property prices, the dealer found it difficult to make profit from the sale of the remaining part of the land. If the ratio of the perimeter of the remaining land to the perimeter of the original land is 3 : 8, at what price (in ) the remaining part of the land is to be sold such that the dealer makes an overall profit of 10%? (2 marks) (1) 500/sq. ft. (2) 550/sq. ft. (3) 600/sq. ft. (4) 650/sq. ft. (5) None of the above.
A property dealer bought a rectangular piece ofland at 1000/sq. ft. The length of the plot is lessthan twice its breadth. Due to its size, there wereno buyers for the full plot. Hence he decided tosell it in smaller sized pieces as given below.The largest square from one end was sold at1200/sq. ft. From the remaining rectangle thelargest square was sold at 1150/sq. ft.Due to crash in the property prices, the dealerfound it difficult to make profit from the sale ofthe remaining part of the land. If the ratio of theperimeter of the remaining land to the perimeterof the original land is 3 : 8, at what price (in ) theremaining part of the land is to be sold such thatthe dealer makes an overall profit of 10%? (2marks)(1) 500/sq. ft. (2) 550/sq. ft.(3) 600/sq. ft. (4) 650/sq. ft.(5) None of the above.
550 I guess....ratio of sides of original field is 5:3. regards scrabbler
A property dealer bought a rectangular piece ofland at 1000/sq. ft. The length of the plot is lessthan twice its breadth. Due to its size, there wereno buyers for the full plot. Hence he decided tosell it in smaller sized pieces as given below.The largest square from one end was sold at1200/sq. ft. From the remaining rectangle thelargest square was sold at 1150/sq. ft.Due to crash in the property prices, the dealerfound it difficult to make profit from the sale ofthe remaining part of the land. If the ratio of theperimeter of the remaining land to the perimeterof the original land is 3 : 8, at what price (in ) theremaining part of the land is to be sold such thatthe dealer makes an overall profit of 10%? (2marks)(1) 500/sq. ft. (2) 550/sq. ft.(3) 600/sq. ft. (4) 650/sq. ft.(5) None of the above.
A property dealer bought a rectangular piece ofland at 1000/sq. ft. The length of the plot is lessthan twice its breadth. Due to its size, there wereno buyers for the full plot. Hence he decided tosell it in smaller sized pieces as given below.The largest square from one end was sold at1200/sq. ft. From the remaining rectangle thelargest square was sold at 1150/sq. ft.Due to crash in the property prices, the dealerfound it difficult to make profit from the sale ofthe remaining part of the land. If the ratio of theperimeter of the remaining land to the perimeterof the original land is 3 : 8, at what price (in ) theremaining part of the land is to be sold such thatthe dealer makes an overall profit of 10%? (2marks)(1) 500/sq. ft. (2) 550/sq. ft.(3) 600/sq. ft. (4) 650/sq. ft.(5) None of the above.
A property dealer bought a rectangular piece ofland at 1000/sq. ft. The length of the plot is lessthan twice its breadth. Due to its size, there wereno buyers for the full plot. Hence he decided tosell it in smaller sized pieces as given below.The largest square from one end was sold at1200/sq. ft. From the remaining rectangle thelargest square was sold at 1150/sq. ft.Due to crash in the property prices, the dealerfound it difficult to make profit from the sale ofthe remaining part of the land. If the ratio of theperimeter of the remaining land to the perimeterof the original land is 3 : 8, at what price (in ) theremaining part of the land is to be sold such thatthe dealer makes an overall profit of 10%? (2marks)(1) 500/sq. ft. (2) 550/sq. ft.(3) 600/sq. ft. (4) 650/sq. ft.(5) None of the above.
Let length be L and breadth be B squares will be Ist of B^2 2nd of (L-B)^2 and last remaining will be of (2B-L)(L-B) perimeter of remaining/(l+b)=3/8 5b=3l b=(3/5)l total sp=1100/sq ft 1200b^2+1150(l-b)^2+k(l-b)(2b-l)=1100lb; k be SP/sq ft of remaining 1200/25 * 9l^2 + 1150(l- 3l/5)^2+k(l- 3l/5)(6l/5 - l) =1100lb 432l^2+184l^2+k(2l^2/25)=1100* 3l^2/5 432+184+2k/25= 1100*3/5 k=22*25=550/sq ft
Ram prepares solutions of alcohol in water according to customers €™ needs. This morning Ram has prepared 27 litres of a 12% alcohol solution and kept it ready in a 27 litre delivery container to be shipped to the customer. Just before delivery, he finds out that the customer had asked for 27 litres of 21% alcohol solution. To prepare what the customer wants, Ram replaces a portion of 12% solution by 39% solution. How many litres of 12% solution are replaced? (1 mark) (1) 5 (2) 9 (3) 10 (4) 12 (5) 15
