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Hovkial
A number is greater than the square of 44 but smaller than the square of 45. One part of the number is the square of 6 and the number is a multiple of 5. What is the number?

(A) 1810

(B) 1940

(C) 1980

(D) 2080

(E) 2110

Let the number be x.

Then, \(44^2 < x < 45^2\)

or, 1936 < x < 2025 ... (1)

Therefore, the number lies between 1936 and 2025.

It is also given that one part of the number is the square of 6. This means that one factor will be 36.

LCM of 36 and 5 = 180.

Therefore, the number will be a multiple of 180,

i.e., x = 180 x 11 = 1980.

This is the only value that satisfies the condition in equation (1).
ANSWER: (C)
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Hovkial
Hovkial
A number is greater than the square of 44 but smaller than the square of 45. One part of the number is the square of 6 and the number is a multiple of 5. What is the number?

(A) 1810

(B) 1940

(C) 1980

(D) 2080

(E) 2110

Let the number be x.

Then, \(44^2 < x < 45^2\)

or, 1936 < x < 2025 ... (1)

Therefore, the number lies between 1936 and 2025.

It is also given that one part of the number is the square of 6. This means that one factor will be 36.


Certainly not GMAT language.
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VeritasKarishma


Certainly not GMAT language.

This is a practice question. GMAT would use different language.
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Hovkial
A number is greater than the square of 44 but smaller than the square of 45. One part of the number is the square of 6 and the number is a multiple of 5. What is the number?

(A) 1810

(B) 1940

(C) 1980

(D) 2080

(E) 2110

IMHO the highlighted part must be " the number is divisible by the square of 6 " , please check...
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Hovkial
Hovkial
A number is greater than the square of 44 but smaller than the square of 45. One part of the number is the square of 6 and the number is a multiple of 5. What is the number?

(A) 1810

(B) 1940

(C) 1980

(D) 2080

(E) 2110

Let the number be x.

Then, \(44^2 < x < 45^2\)


or, 1936 < x < 2025 ... (1)

Therefore, the number lies between 1936 and 2025.

It is also given that one part of the number is the square of 6. This means that one factor will be 36.

LCM of 36 and 5 = 180.

Therefore, the number will be a multiple of 180,

i.e., x = 180 x 11 = 1980.

This is the only value that satisfies the condition in equation (1).
ANSWER: (C)


"one part of the number is square of 6" could also mean the number has 36 in it. in option 'b', product of 4 and 9 is 36, and its a multiple of 5. i feel answe is 'B'
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