As the sphere will be touching all the 6 faces, the shortest distance will be same and that will be the distance between any edge of cube and the 3 points where sphere touched the cube.
This distance will be half of a diagonal of cube i.e sqrt (10^2 + 10^2) = 5.(sqrt2) = 7.07
The only option which is near to this is 10( 1) = 7.32
Whats the OA ?
Dopa,
The OA is D.
I marked E.. my explanation... since spheres is inscribed in cube. consider the top surface.. it will be more like a circle in square. and we are asked to find the minimum distance b/w one of vertices to the surface area of circle.
Sol = (Length of diagonal of Square)/2 - Radius of Square. = (sqrt(200)/2) - 5 = 5 (sqrt(2) - 1)
The orignial solution is:
The shortest distance from a vertex of the cube to the sphere would be the length of the diagonal of the cube minus the radius of the sphere. To understand why, think of the parallel situation in two dimensions. In the diagram of the circle inscribed in the square to the right, the shortest possible distance from one of the vertices of the square to the circle would be the diagonal of the square minus the radius of the circle.
The diagonal of a cube of side x is x. This can be found by applying the Pythagorean Theorem twice (first to find the diagonal of a face of the cube, x, and then to find the diagonal through the center, x). Like the sides of the circle in the diagram above, the sides of a sphere inscribed in a cube will touch the sides of the cube. Therefore, a sphere inscribed in a cube will have a radius equal to half the length of the side of that cube.
Diagonal of the cube = x = 10 Radius of the sphere = 5 diagonal of the cube radius of the sphere = 5 5 = 5( 1)
its a cube & you are considering it as square. Diagonal of cube is 10Sqrt(3) hence the shortest distance will be
Shortest distance = 5Sqrt(3) - 5 = 5(Sqrt(3) 1)
Cheers....
I think the answer should be E.
As the sphere will be touching all the 6 faces, the shortest distance will be the distance between any edge of cube and the point where sphere touched the cube minus the radius of sphere.
This distance will be half of a diagonal of cube i.e sqrt (10^2 + 10^2) = 5.
its a cube & you are considering it as square. Diagonal of cube is 10Sqrt(3) hence the shortest distance will be
Shortest distance = 5Sqrt(3) - 5 = 5(Sqrt(3) 1)
Cheers....
Hi.. even though its a cube.. visualising a sphere in a cube.. if we were asked the question of minimal distance b/w cube's vertex and surface of sphere.. we have various options.. 1. vertex and where the sphere touches the cube - 5 2. vertex and toward inside of cube .. 5(Sqrt(3) 1) - like u said 3. vertex and towards the cube's face or base - 5(Sqrt(2) 1)
of all these .. '3' yields the minimal value... hence i picked 3..
Please let me know if iam missing something. Thanks
3. I cudnt find any that matches the answer.. The length of each red stick is 19 inches less that the average length of the sticks in Box W => r = (average length of box W) - 19 => average length of box W = r + 19 and 6 inches greater than the average length of the sticks in Box V. => r = (average length of box V) + 6 => average length of box V = r - 6 What is the average (arithmetic mean) length, in inches, of the sticks in Box W minus the average length, in inches, of the sticks in Box V? average length of box W - average length of box V = (r+19) - (r-6) = 25..
yeah thnx for 1 & 2...but not sure of Q3...even i followed the same approach but cudnt reach a soln.... m hoping if someone can help on this ques.....
All DS questions below ======================= Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year? (1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets. (2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
At a fruit stand yesterday, the price of each apple was $0.10 more than the price of each orange. What was the total revenue from the sale of oranges at the fruit stand yesterday? (1) The number of oranges sold at the fruit stand yesterday was 5 more than the number of apples. (2) The total revenue from the sale of apples at the fruit stand yesterday was $15.00
If the average (arithmetic mean) of the assessed values of x houses is $212,000 and the average of the assessed values of y other houses is $194,000, what is the average of the assessed values of the x+y houses? (1) x+y=36 (2) x=2y A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year? (1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets. (2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
At a fruit stand yesterday, the price of each apple was $0.10 more than the price of each orange. What was the total revenue from the sale of oranges at the fruit stand yesterday? (1) The number of oranges sold at the fruit stand yesterday was 5 more than the number of apples. (2) The total revenue from the sale of apples at the fruit stand yesterday was $15.00
If the average (arithmetic mean) of the assessed values of x houses is $212,000 and the average of the assessed values of y other houses is $194,000, what is the average of the assessed values of the x+y houses? (1) x+y=36 (2) x=2y A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
hi abouttime, please ask the question in proper thread this one not for DS....... any way its answer shoud be D.......... what is OA
All DS questions below ======================= Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year? (1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets. (2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
At a fruit stand yesterday, the price of each apple was $0.10 more than the price of each orange. What was the total revenue from the sale of oranges at the fruit stand yesterday? (1) The number of oranges sold at the fruit stand yesterday was 5 more than the number of apples. (2) The total revenue from the sale of apples at the fruit stand yesterday was $15.00
If the average (arithmetic mean) of the assessed values of x houses is $212,000 and the average of the assessed values of y other houses is $194,000, what is the average of the assessed values of the x+y houses? (1) x+y=36 (2) x=2y A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
Q1) Answer is D from stem 1: we knw no. of cos which reported net profit = 21, hence only net profit = 21-12 = 9 no. of cos which reported which invested n foreign markets = 15; hence only foreign markets = 3 hence no. of cos which reported profits or invested in foreign markets or both = 9+12+3 = 24 hence no. of cos which did neither = 6....suff stem 2: implies same....suff
Hence D
Q2) Both statements fail to convey the ratio of apples to oranges, hence the total revenue from sale of oranges cannot be found.
distance between one edge of cube and surface of sphere which touches the cube = 5( 1)
distance between one edge of cube and the internal surface of sphere = 5( 1)
The question has asked for shortest distance so the answer should be E.
I may be going wrong somewhere
The sphere will touch each of the cube's faces at one and only one point each; anyways the shortest distance from the vertex to the surface of the sphere will lie on the diagonal of the cube which is also where the center of the sphere is located. we can also use the Pythagoras here.. vertex to center of sphere : Hypotenuse center to face of cube adjacent to vertex : radius = 5 the above makes a 90 degree angle with the line joining this point on the face back to the vertex, which is half the diagonal.
the hypotenuse minus the radius gives you the shortest distance.
distance between one edge of cube and surface of sphere which touches the cube = 5( 1)
distance between one edge of cube and the internal surface of sphere = 5( 1)
The question has asked for shortest distance so the answer should be E.
I may be going wrong somewhere
"distance between one edge of cube and surface of sphere which touches the cube = 5( 1)" this is where you are wrong. this distance would be half of length of face diagonal ( 10/2 = 5 ) you do not subtract 5 from it. i hope this helps.
Q. Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit?
How can we use the method of 1 - (always together) in this question?
Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year? (1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets. (2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
At a fruit stand yesterday, the price of each apple was $0.10 more than the price of each orange. What was the total revenue from the sale of oranges at the fruit stand yesterday? (1) The number of oranges sold at the fruit stand yesterday was 5 more than the number of apples. (2) The total revenue from the sale of apples at the fruit stand yesterday was $15.00
If the average (arithmetic mean) of the assessed values of x houses is $212,000 and the average of the assessed values of y other houses is $194,000, what is the average of the assessed values of the x+y houses? (1) x+y=36 (2) x=2y
Q1. Both the stats r sufficient to ans; so 'd'
Q2. can not be ans using either of the stat or combining both of them; ans 'e'
Q1. If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Q2. If x 7 A. -x B. -1 C. 1 D. x E. x Q3:From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected? A.1/10 B. 4/9 C.1/2 D.3/5 E.2/3 Q4. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? A. 5 B. 6 C. 7 D. 8 E. 9 Q5. Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m? A. k m % B. (k m) % C. / (100 + k) % D. / (100 + m) % E. / (100 + k + m) %
Q. Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit?
How can we use the method of 1 - (always together) in this question?
Regards MSD
Hi,
Not all questions are easily solvable using this technique... some become hard.. if not solvable..
Going by your method.. it actually should have been... = (Total no. of ways they can sit) - (atleast one dwarf is sitting next to another dwarf or atleast one dwarf is sitting next to another elve) .
Alternatively, this can be solved as:
consider DEDEDE --> six positions...
consider dwarf position are fixed.. they can arrange themselves in 3! = 6 ways. We have 3 positions left.. and three elves to fill in... gives 3! ways = 6 Total number of ways = 6 * 6 = 36.
Considering elves position as fixed.. we get another 36. Solution would be 72 ways..
Q1. If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Q2. If x 7 A. -x B. -1 C. 1 D. x E. x Q3:From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected? A.1/10 B. 4/9 C.1/2 D.3/5 E.2/3 Q4. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? A. 5 B. 6 C. 7 D. 8 E. 9 Q5. Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m? A. k m % B. (k m) % C. / (100 + k) % D. / (100 + m) % E. / (100 + k + m) %
1. E
different 5 letter words = 10 * 9 * 8 * 7 * 6 different 4 letter words = 10 * 9 * 8 * 7
Ratio = 6 : 1
2. A
Let x = -4
sqrt ( -(-4) -4) = 4 = -x
3. D
No of ways to pick 4 children = 6C4 = 15 No of ways to select 2 girls of 3 = 3C2 = 3 No of ways to select 2 boys of 3 = 3C2 = 3
Sol = (3*3)/ 15 = 3/5
4. D - 8 ways.
5. D let price per share be 'a' earning per share be 'b'
Prior to Increase: Ratio of price per share to earning per share is (a/b) Post Increase: Ratio --> (a + (a *k/100)) / (b + (b *m/100)) => (a/b) (1+k/100)(1+m/100) => (a/b) (100+k/100+m)
Lets say, increase % be t => (a/b) + (a/b) * (t/100) = (a/b) (100+k/100+m) => 1 + (t/100) = (100+k/100+m) solving for t, we get t = (k-m) (100) / (100+m)
Q1. If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Q2. If x 7 A. -x B. -1 C. 1 D. x E. x Q3:From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected? A.1/10 B. 4/9 C.1/2 D.3/5 E.2/3 Q4. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? A. 5 B. 6 C. 7 D. 8 E. 9 Q5. Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m? A. k m % B. (k m) % C. / (100 + k) % D. / (100 + m) % E. / (100 + k + m) %
different 5 letter words = 10 * 9 * 8 * 7 * 6 different 4 letter words = 10 * 9 * 8 * 7
Ratio = 6 : 1
2. A
Let x = -4
sqrt ( -(-4) -4) = 4 = -x
3. D
No of ways to pick 4 children = 6C4 = 15 No of ways to select 2 girls of 3 = 3C2 = 3 No of ways to select 2 boys of 3 = 3C2 = 3
Sol = (3*3)/ 15 = 3/5
4. D - 8 ways.
5. D let price per share be 'a' earning per share be 'b'
Prior to Increase: Ratio of price per share to earning per share is (a/b) Post Increase: Ratio --> (a + (a *k/100)) / (b + (b *m/100)) => (a/b) (1+k/100)(1+m/100) => (a/b) (100+k/100+m)
Lets say, increase % be t => (a/b) + (a/b) * (t/100) = (a/b) (100+k/100+m) => 1 + (t/100) = (100+k/100+m) solving for t, we get t = (k-m) (100) / (100+m)
Hope it helps...
dear alchemist, cud u explain the 4th ques.
further what r the resources frm which u r practising P&C;, prob and stats?
further what r the resources frm which u r practising P&C;, prob and stats?
thanks
Two possibilities:
1. One of the offices has 3 employees and other one has none - striaght forward 2 ways 2. One of the office has 1 employee and the other office has 2 employees - 6 ways. let a,b,c be the employees... arrangements.... (a, bc) (b,ac) (c,ab) (ab,c) (ac,b) (bc,a).
hope this helps.
regard to ur question on practice... a lil' of everywhere.... OG, kaplan.. and solving few questions in forums 😃
Q. Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit?
How can we use the method of 1 - (always together) in this question?
Regards MSD
no. of ways = total no of ways of seating the 6 - no of ways the dwarfs and elves can be seated together
total no of ways of seating 6 = 6!
consider the dwarfs and elves to be single units. therefore the 2 groups can be seated in 2! ways. Now within each group the dwarfs can be arranged in 3! ways and elves can be arranged in 3! ways.
no of ways dwarfs and elves can be seated together is 2! x 3! x 3! = 72 ways
no. of ways = total no of ways of seating the 6 - no of ways the dwarfs and elves can be seated together
total no of ways of seating 6 = 6!
consider the dwarfs and elves to be single units. therefore the 2 groups can be seated in 2! ways. Now within each group the dwarfs can be arranged in 3! ways and elves can be arranged in 3! ways.
no of ways dwarfs and elves can be seated together is 2! x 3! x 3! = 72 ways
answer = 6! - 72 = 720 - 72 = 648
what is the OA?
krajkumar6,
If you were to follow this approach.. I guess you should include (in you minus calcuation) the following scenario too -- when two dwarfs (elves) sit together and one dwarf (elv) sits alone... for eg.. DDEEED.
1) = 7.32
, and then to find the diagonal through the center, x