Q1. N & Y are positive integers and 450y=n^3, which is an integer?
y/3*2^2*5
y/3^2*2*5
y/3*2*5^2
A. None
B.I
C. II
d.III
e. I, II, III
Q2- A thin piece of 40m wire is cut in two. one piece is a circle with radius r. other is a square. no wire is left over. which represents total area of circle and square in terms of r?
a. Pie r^2
b.Pie r^2+10
c. Pie r^2+1/4 Pie^2r^2
d. Pie r^2+ (40-2 pie. r)^2
e.Pie r^2+( 10-1/2pie .r)^2
Q3- if each term in the series a1+a2+......+aN is eithe 7 or 77, and the sum equals 350. which of the following cud b equal to N?
A.38
B.39
C.40
D.41
E.42
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Question #1 is solved here - https://www.beatthegmat.com/n-y-are-posi ... 52635.html
Question #2 is solved here - https://www.beatthegmat.com/area-of-circ ... 85340.html
Question #3 is solved here - https://www.beatthegmat.com/sum-a1-a2-a3-an-t109893.html
Please let me know if need any further help!
Question #2 is solved here - https://www.beatthegmat.com/area-of-circ ... 85340.html
Question #3 is solved here - https://www.beatthegmat.com/sum-a1-a2-a3-an-t109893.html
Please let me know if need any further help!
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450y=n^3 implies (3^2 * 5^2 * 2)y = n^3, which implies y should be 2^2 * 3 * 5 so that 450y=n^3intenseCK wrote:Q1. N & Y are positive integers and 450y=n^3, which is an integer?
y/3*2^2*5
y/3^2*2*5
y/3*2*5^2
A. None
B.I
C. II
d.III
e. I, II, III
Then (I) will be an integer.
(II) and (III) will not be an integer always.
The correct answer is B.
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Perimeter of the circle = 2Ï€rintenseCK wrote: Q2- A thin piece of 40m wire is cut in two. one piece is a circle with radius r. other is a square. no wire is left over. which represents total area of circle and square in terms of r?
a. Pie r^2
b.Pie r^2+10
c. Pie r^2+1/4 Pie^2r^2
d. Pie r^2+ (40-2 pie. r)^2
e.Pie r^2+( 10-1/2pie .r)^2
Therefore, perimeter of the square = (40 - 2Ï€r)
Hence, length of each side of the square = (40 - 2πr)/4 = (10 - πr/2)
Therefore, total area of circle and square = (Area of the circle) + (Area of the square) = πr² + (10 - πr/2)²
The correct answer is E.
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intenseCK wrote: Q3- if each term in the series a1+a2+......+aN is eithe 7 or 77, and the sum equals 350. which of the following cud b equal to N?
A.38
B.39
C.40
D.41
E.42
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Let x and y be the number of 7's and the number of 77's respectively.
Then 7x + 77y = 350 implies x + 11y = 50
x + y = 50 - 10y
So, x + y = n = 50 - 10y implies n must have the unit digit of 0 because 50 - 10y must be a number which has units digit as 0. C is the only option in which the units digit is 0.
The correct answer is C.
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Hi Anurag- can u elaborate a little more as i am struggling to get your logic. why shd Y be 2^2*3*5Anurag@Gurome wrote:450y=n^3 implies (3^2 * 5^2 * 2)y = n^3, which implies y should be 2^2 * 3 * 5 so that 450y=n^3intenseCK wrote:Q1. N & Y are positive integers and 450y=n^3, which is an integer?
y/3*2^2*5
y/3^2*2*5
y/3*2*5^2
A. None
B.I
C. II
d.III
e. I, II, III
Then (I) will be an integer.
(II) and (III) will not be an integer always.
The correct answer is B.
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450y is the cube of an integer.If n and y are positive integers and 450y = n³, which of the following must be an integer?
I. y/(3 x 2² x 5)
II. y/(3² x 2 x 5)
III. y/(3 x 2 x 5²)
a. None
b. I only
c. II only
d. III only
e. I, II, and III
When we prime-factorize the cube of an integer, we get 3 (or a multiple of 3) of every prime factor:
8 is the cube of an integer because 8 = 2³ = 2*2*2.
27 is the cube of an integer because 27 = 3³ = 3*3*3.
Thus, when we prime-factorize 450y, we need to get at least 3 of every prime factor:
450y = 2 * 3² * 5² * y
Since 450 provides only one 2, two 3's, and two 5's, y must provide the missing prime factors. We need y to provide two more 2's, one more 3, and one more 5.
Thus, the smallest possible value is y = 2² * 3 * 5.
Onto the answer choices:
I. y/(3 x 2² x 5)
(2² * 3 * 5)/(3 x 2² x 5) = 1. The smallest possible value of y yields an integer.
Eliminate every answer choice that does not include I.
Eliminate A, C and D.
II. y/(3² x 2 x 5)
(2² * 3 * 5)/(3² x 2² x 5) = 1/3. Not an integer.
Eliminate every remaining answer choice that includes II.
Eliminate E.
The correct answer is B.
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