Question 1 :
If 8575 = 5^{x }⋅ 7^{y}, what is (xy) - 5 ?
(A) 1 (B) 3 (C) 6 (D) 7 (E) 12
Solution :
First, let us find the prime factors of 8575.
8575 = 5^{2 }⋅ 7^{3}
x = 2 and y = 3
xy - 5 = 2(3) - 5
= 6 - 5
= 1
Hence the answer is 1.
Question 2 :
When d is divided by 8, the remainder is 3. What is the remainder when d + 3 is divided by 8 ?
(A) 1 (B) 3 (C) 4 (D) 6 (E) 7
Solution :
Let d = 11
Here we choose 11, because it is greater than 8, when we divide 11 by 8, we get the remainder 3.
Then d + 3 = 11 + 3 = 14
By dividing this d + 3 by 8, we get 6(3 + 3) as remainder.
Hence the answer is 6.
Note : The number chosen should be 3 more than the multiple of 8.
Question 3 :
Tommy is making as 6 letter password using only the letters A, B, C, D, E and F. How many different codes can Tommy make, if every letter can only be used once in each code ?
(A) 1 (B) 6 (C) 120 (D) 720 (E) 46, 656
Solution :
Let us mark 6 blank spaces.
____ ____ ____ ____ ____ ____
The first letter chosen be placed in any of the above 6 dashes.
Now, we have remaining 5 letters.
The second letter chosen, out of 5 may be placed in any one of the remaining 5 places.
In this way, we may create 6! codes by using 6 letters.
Hence the answer is 720.
Question 4 :
-5 (x -3) ≥ 20 what is the solution to the inequality shown above ?
(A) x ≥ -1 (B) x ≥ 7 (C) x ≤ -1 (D) x ≤ 7 (E) x ≥ 1
Solution :
-5 (x -3) ≥ 20
-5x + 15 ≥ 20
Subtract 15 on both sides, we get
-5x ≥ 20 - 15
-5x ≥ 5
Divide by -5 on both sides, we get
x ≤ -1
Question 5 :
Which numbers line below shows the solution to the inequality -2 < x/3 ≤ 2 ?
Solution :
= -2 < x/3 ≤ 2
Multiply the entire inequality by 3. So we get,
= -6 < x ≤ 6
The fourth option represents the the solution which is greater than -6 and less than or equal to 6.
Question 6 :
There are 15000 teens whose favorite genre is comedy. How many teens have a favorite genre of action ?
(A) 30 (B) 41,250 (C) 52,500
(D) 56,250 (E) 70,000
Solution :
Let "x" be the total population
8% of x = 15000
0.08 x = 15000
x = 15000/0.08
x = 187500
The number of teens whose genre is action
= 30% of 187500
= 56250
Question 7 :
A computer originally prices at $550.50 is on sale for 20% off. Jamie used a 5% discount coupon which was applied to the sales price. How much did Jamie pay for the computer ?(Assume there is no tax)
(A) $412.88 (B) $418.38 (C) $440.40
(D) $522.98 (E) 539.49
Solution :
Original price of computer = $550.50
From the 100% of price, the shop is going to give 20% off. Hence we have to pay 80% of the original price for the computer.
80% of 550.50 = $440.40
Again we have 5% discount, so we have to calculate 95% of discounted price.
0.95 (440.40) = 418.38
Hence the final amount for the computer is 418.38.
Question 8 :
Given the following value 4, 760 solve the following, x^{2}/y, if x represents the smallest prime factor of the given value and y represents the greatest prime factor of the given value.
(A) 119/4 (B) 4/17 (C) 2/119 (D) 4/119 (E) 2/17
Solution :
4760 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 7 ⋅ 17
Smallest prime factor = 2, largest prime factor = 17
x^{2}/y = 2^{2}/17 = 4/17
Hence the answer is 4/17.
Question 9 :
An adult male Diptera has a mass of 11.5 milligrams. What is the Diptera's mass in grams?
(A) 0.0115 g (B) 0.115 g (C) 1.15 g
(D) 11.5 g (E) 115 g
Solution :
1000 milli grams = 1 gram
= (11.5/1000) grams
= 0.0115 grams.
Question 10 :
Michel has a project due in exactly 83 hours. It is currently 8 : 30 on Monday morning. What time is his project due ?
(A) 6:30 PM Friday (B) 7:30 PM Friday
(C) 7:30 AM Thursday
(D) 7:30 PM Thursday (E) 9:30 PM Thursday
Solution :
Every day consists of 24 hours. In 83 hours, we have three consecutive days and 11 hours remaining.
It is currently 8 : 30 on Monday morning.
Then, we have
Monday (8:30 A.M) to Tuesday (8 : 30 A.M) ==> 24 hours
Tuesday (8:30 A.M) to Wednesday (8 : 30 A.M) ==> 24 hours
Wednesday (8:30 A.M) to Thursday (8 : 30 A.M) ==> 24 hours
Thursday 8:30 A.M + 11 hours = Thursday 7.30 P.M.
So, the project is due at 7.30 pm Thursday.
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