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261 / 652
I bought a certain number of marbles at a rate of 27 marbles for rupees 2 times M,where M is an integer. I divided these marbles into 2 parts of equal numbers,one part of which I sold at the rate of 13 marbles for Rs.M and the other at the rate of 14 marbles for Rs.M.I spent and received an integral no of rupees,but bought the least number of marbles.How many did I buy?
A870
B9828
C9288
D9838
Answer: Option B
Explanation:Let he bought x marbles.
27 marbles costs = Rs. 2M
Therefore, x marbles costs = Rs. (2M * x) / 27
Since the marble is divided into 2 equal parts so the number x should be an even number.
For first x/2 marbles,
13 marbles s.p. is = Rs. M
Therefore, x/2 marbles s.p. = Rs. (M * x) / 26
For other x/2 marbles,
14 marbles s.p. is = Rs. M
Therefore, x/2 marbles s.p. = Rs. (M * x) / 28
Now we can't equate like [(M * x) / 26] + [(M * x) / 28] = (2M * x) / 27
because (M *x ) will get cancel each side and of course 1/28 + 1/26 is not equal to 2/27
So here we don't need M and we can cancel it.
After that we have,
CP = 2x/27
For first x/2 marbles,
SP = x/26
And for other x/2 marbles,
SP = x/28
Now this CP and SP must be an integer (as per question). So we have to find a number x which will be divisible simultaneously by 27, 26 and 28. So we have to find the LCM of 26, 27, 28 which will turn out minimum value as 9828 and it is even as well. So the value of x will be 9828 minimum.
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262 / 652
A sudoku grid contains digits in such a manner that every row, every column, and every 3x3 box accommodates the digits 1 to 9, without repetition. In the following Sudoku grid, find the values at the cells denoted by x and y and determine the value of 6x + 15y.
A87
B75
C66
D99
Answer: Option B
Explanation:So x = 5, y = 3.
6x + 15y = 75
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263 / 652
How many different integers can be expressed as the sum of three distinct numbers from the set {3, 8, 13, 18, 23, 28, 33, 38, 43, 48}?
A22
B8
C56
DNone of these
Answer: Option A
Explanation:minimum possible number = 24 ( 3+8+13)
maximum possible number = 129 ( 38+43+48)
so if we assume a AP series now where common difference is 5 and the series will start with 24 and last term will be 129 then, using AP formula
Total numbers = [(l-a)/d + 1] = [(129 - 24)/7+1 ] = 22
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264 / 652
There is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save. Auggie was very curious to test this theory.Auggie spent all of his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?
A248
B120
C252
D250
Answer: Option A
Explanation:As he has spent all his money, He must spend Rs.8 in the final store.
a simple equation works like this. Amount left = 1/2 x?4
For fifth store this is zero. So x = 8. That means he entered fifth store with 8.
Now for fourth store, amount left = 8 so 1/2 x?4=8=> x = 24
For third store, amount left = 24 so 1/2 x?4=24=> x = 56
For Second store, amount left = 56 so 1/2 x?4=56=> x = 120
For first store, amount left = 120 so 1/2 x?4=120=> x = 248
So he entered first store with 248.
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265 / 652
HCF of 2472,1284 and a third number 'n'is 12.If their LCM is 8*9*5*103*107.then the number 'n'is..
A2^2*3^2*5^1
B2^2*3^2*7^1
C2^2*3^2*8103
DNone of these
Answer: Option A
Explanation:2472 = 2^3×3×103
1284 = 2^2×3×107
HCF = 2^2×3
LCM = 2^3×3^2×5×103×107
HCF of the numbers is the highest number which divides all the numbers. So N should be a multiple of 2^2×3
LCM is the largest number that is divided by the given numbers. As LCM contains 32×5 these two are from N.
So N = 2^2×3^2×5^1
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266 / 652
What is the value of 77!*(77!-2*54!)^3/(77!+54!)^3+54!*(2*77!-54!)^3/(77!+54!)^3
A77! - 54!
B77! + 54!
C77!^2 - 54!^2
D77!
Answer: Option A
Explanation:take 77!=a
and 54!=b
now the given expression will look like
(a(a-2b)^3 )/(a+b)^3 + (b(2a-b)^3 )/(a+b)^3
( a (a^3 - 6a^2 b + 12ab^2 - 8b^3) + b (8a^3 - 12a^2 b + 6ab^2 - b^3) ) / (a+b)^3
(a^4 - 6a^3 b + 12 a^2 b^2 - 8ab^3 + 8a^3 b - 12a^2 b^2 + 6ab^3 - b^4) / (a+b)^3
(a^4 + 2a^3 b - 2ab^3 - b^4) / (a+b)^3
( a^4 - b^4 + 2ab(a^2 - b^2) ) / (a+b)^3
( (a^2 + b^2)(a^2 - b^2) + 2ab(a^2 - b^2) ) / (a+b)^3
( (a^2 - b^2) (a^2 + b^2 + 2ab) ) / (a+b)^3
( (a^2 - b^2)(a+b)^2 ) / (a+b)^3
( (a+b)(a-b) (a+b)^2 ) / (a+b)^3
( (a+b)^3 (a-b) ) / (a+b)^3
a-b
i.e 77! - 54!
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267 / 652
The marked price of coat was 40% less than the suggested retail price. Eesha purchased the coat for half of the marked price at the 15th anniversary sale. What percent less than the suggested retail price did Eesha pay?
A0.6
B0.2
C0.7
D0.3
Answer: Option C
Explanation:Let the retail price = 100
So the market price will be = (100 - 40)% (100) = 60
Easha purchased price = 60/2 = 30
So she bought it for 70% less than retail price.
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268 / 652
A spherical solid ball of radius 58 mm is to be divided into eight equal parts by cutting it four times longitudinally along the same axis.Find the surface area of each of the final pieces thus obtained( in mm^2) ? (where pi= 22/7)
A3365pi
B5046pi
C1682pi
D3346pi
Answer: Option B
Explanation:If a sphere is cut into 8 parts longitudinally, It something looks like below Now We have to find the surface area of one piece. This is 1/8th of the initial sphere + 2 × area of the half circle
= 1/8(4?r^2)+?r2
= 1/8(4 * ? * (58)^2) + ? *(58)^2
= 5046pi
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269 / 652
In a city there are few engineering, MBA and CA candidates. Sum of four times the engineering, three times the MBA and 5 times CA candidates is 3650. Also three times CA is equal to two times MBA and three times engineering is equal to two times CA. In total how many MBA candidates are there in the city?
A200
B300
C450
D400
Answer: Option C
Explanation:Lets assume number of engg = e
number of Mba = m
and Number of CA = c
4e+3m+5c=3650
3c=2m m=3c/2
3e=2c e=2c/3 ------------- (1)
put the value in the above eq. (1)
4*2c/3+3*3c/2+5c=3650
c=300
m=3c/2
m=450
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270 / 652
A rectangle is divided into four rectangles with area 70, 36, 20, and x. The value of x is
A350/9
B350/7
C350/11
D350/13
Answer: Option A
Explanation:Areas are in proportion.
70/x = 36/20
=> x = 350/9
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