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Which of the following is a common factor of both x2 – 4x – 5 and x2 – 6x – 7?
(A) x – 5
(B) x – 7
(C) x – 1
(D) x + 5
(E) x + 1 |
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x 2 – 4x – 5 = (x – 5)(x + 1), and x 2 – 6x – 7 = (x – 7)(x + 1). The common factor is x + 1, choice (E).
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If log 2 = 0. 3010, then find how many digits are contained in the number 256. |
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To find the number of digits contained in the number, increment the characteristic (integral part) of the logarithmic value of the number by one.
Taking log of the given number, we get log 2 56 = 56* log 2 = 56 * 0. 3010 = 16. 85.
Here the characteristic (integral part) = 16.Therefore, number of digits contained in the number 2 56 is 16 + 1 = 17.
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When the units and tens digits of a certain two-digit number are reversed, the sum of the two numbers is 121 and the difference is 9. What is the tens digit of the original number?
A. 1
B. 3
C. 4
D. 6
E. 7 |
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The correct answer is (D). Calling the number 10t + u, when we reverse the digits, we get 10u + t. The sum is then (10t + u) + (10u + t) = 11t + 11u = 121. Dividing by 11, we have t + u = 11. Taking the difference: (10t + u) – (10u + t) = 9t – 9u = 9, and dividing by 9: t – u = 1. Finally, adding: t + u = 11
t – u = 1
2t = 12 t = 6
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If two similar triangles have bases in the ratio of 2:3, what is the ratio of their areas?
A. 1:1.67
B. 2:3
C. 4:6
D. 4:9 |
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Correct answer is (D). Area is proportional to square of the sides.
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A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
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Red light flashes every 20 seconds, Green light flashes every 24 seconds.
Therefore, they will flash together after LCM of 20 and 24 i.e. every 120 seconds. In every hour they will flash 3600/120 = 30 times
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