divelab/Sys2Bench huggingface dataset:
Question: A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 65 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
Options:
A) 5
B) 6
C) 7
D) 8
E) 9
Rationale: answer is C ...7 dozens ....
half sold by noon --> 20 dozens (20 *12 =240)
remaining --> 20 dozens i.e 240 eggs...
65% sold --> 65*240/100 =156 eggs
remaining 35 % --> 84 eggs (7 dozens ) --> answer
Answer: C
Question: A candy company sells premium chocolate at $5 per pound and regular chocolate at $2 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box?
Options:
A)[A] 1
B)[B] 2
C)[C] 3
D)[D] 4
E)[E] 5
Rationale: This question is a bit of Special equations with a single set of unique values.
the Equation stands : 5X + 2Y = 31
Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4
31 - 5 = 26 -> Not divisible by 4
31 - 10 = 21 -> Not divisible by 4
31 - 15 =16 -> Divisible by 4
31 - 20 =11 -> Not divisible by 4
31 - 25 =6 -> Not divisible by 4
31 - 30 =1 -> Not divisible by 4
Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible
Thus Amount spent on regular chocolate= $16
Amount spent on Premium chocolate= $15
Price per premium chocolate = $5
No. Of boxes of premium chocolate bought = 10 / 5 = 2
Correct Option : B
Answer: B
Question: A company, Chauncy Co., has an annual travel budget of $50,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
Options:
A)Expenses will not go over the budget.
B)$500
C)$4,225
D)$5,725
E)$10,725
Rationale: annual travel budget of $50,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 50000-60725 = 10725
Answer: Option E
Answer: E
Question: The cost of an item is Rs 12.60. If the profit is 10% over selling price what is the selling price ?
Options:
A)13 rupees
B)17 rupees
C)16 rupees
D)15 rupees
E)14 rupees
Rationale: C.P+PROFIT=S.P
given,
PROFIT=10*S.P/100
so, S.P=12.60+10*S.P/100
90*S.P=1260
S.P=14 rupees
ANSWER:E
Answer: E
Question: Two cars start at the same time from opposite ends of a highway that is 105 miles long. One car is riding at 15 mph and the second car is riding at 20 mph. How long after they begin will they meet?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 20+15 = 35 mph
Total distance to be covered = 105 miles.
Time taken would be: 105 miles/35 mph = 3 hours
C is the answer.
Answer: C
Question: A vendor bough toffees at 6 for a rupee. how many for a rupee must he sell to gain 20%?
Options:
A)3
B)8
C)5
D)9
E)1
Rationale: C.P or toffees = Rs.1, S.P of 6 toffee = 120% of Rs.1 = Rs.6/5
for Rs. 6/5, toffees sold=6, for Rs.1, toffees sold= (6*5/6)= 5
Correct answer (C)
Answer: C
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
Options:
A)191
B)213
C)221
D)223
E)226
Rationale: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 10% of the cost:
Sell Price = Cost + $30
Sell Price = $300 + $30
Thus, the Sell Price is $330 for each item. Selling all 100 items gives the retailer...
100($30) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(330) = $16.5 discount
$313.5 = $300 + $13.5
Now, the retailer makes a profit of just $13.5 per item sold.
To earn $2,000 in profit, the retailer must sell....
$13.5(X) = $2,000
X = 2,000/13.5
X = 222.222222 items
You'll notice that this is not among the answer choices.... 221 and 223 are.
Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.
Final Answer:
D
Answer: D
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
Options:
A)Rs. 20
B)Rs. 15
C)Rs. 22.50
D)Rs. 7.50
E)None of these
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.
ANSWER:B
Answer: B
Question: A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.
Options:
A)40 cm/m
B)15 cm/m
C)10 cm/m
D)35 cm/m
E)20 cm/m
Rationale: The volume of a rectangular prism is given by
area of base ? height
The rate at which the tank is being filled is 1 liter per minute which we need to convert
1 liter = 1 dm3
But 1 dm = 10 cm. Hence
1 liter = (10 cm)3 = 1000 cm3
The height h of the water is related to the volume by
volume = area of base ? h
In one minute the volume increases by 1 liter or 1000 cm3 and the height increases by
h = volume / area of base = 1000 cm3 / 100 cm2 = 10 cm
correct answer C
Answer: C
Question: An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
Options:
A)8.04%
B)8.14%
C)8.23%
D)8.16%
E)8.5%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(104)2 - (100)2]
= (104 + 100) x (104 - 100)
= 816 cm2.
Percentage error = 8.16
D
Answer: D
Question: How much 60% of 50 is greater than 30% of 30?
Options:
A)21
B)91
C)11
D)17
E)12
Rationale: (60/100) * 50 – (30/100) * 30
30 - 9 = 21
Answer: A
Answer: A
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)10 m
B)16 m
C)245 m
D)19 m
E)235 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30
= 25/2 => 2(140 + x) = 750 => x
= 235 m.
Answer: E
Answer: E
Question: 2a
33
+ b9
____
99
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 3b ?
Options:
A)2
B)7
C)9
D)11
E)12
Rationale: Adding the digits in unit's place , a+ 3 + 9 = 19 (Since a and b are positive single digits )
=> a = 7
Now adding the digits in ten's place , 2+ 3 + b + 1= 9 (1 has been carried over from nit's place addition)
=> b= 3
a+3b = 2+2*3
=11
Answer D
Answer: D
Question: A goat is tied to one corner of a square plot of side 12m by a rope 7m long. Find the area it can graze?
Options:
A)32
B)36.5
C)38.5
D)39
E)39.5
Rationale: Area covered by goat = Pi*r^2/4 ( here we divide by 4 because rope is tied at the corner of the plot and only 1/4 part , the goat can graze)
where r= 7 m = length of rope
So area = (22/7)*7*7/4 = 38.5 sq m
answer :C
Answer: C
Question: Find the constant k so that : -x2 - (k + 8)x - 8 = -(x - 2)(x - 4)
Options:
A)11
B)12
C)14
D)19
E)15
Rationale: -x2 - (k + 8)x - 8 = -(x - 2)(x - 4) : given
-x2 - (k + 8)x - 8 = -x2 + 6x - 8
-(k + 8) = 6 : two polynomials are equal if their corresponding coefficients are equal.
k = -14 : solve the above for k
correct answer C
Answer: C
Question: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is?
Options:
A)5 5/11%
B)6%
C)7%
D)8%
E)9%
Rationale: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % = 300/5500 x 100	%	= 5	5/11	%
A)
Answer: A
Question: There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimetres then the area (in square centimetres) of the triangle ABC would be
Options:
A)π√​12
B)9/π
C)9√3/π
D)6√3/π
E)None of these
Rationale: Explanation :
Outer circle:
Since πR² = 12, R = √(12/π) = 2√(3/π).
Inner circle:
Since the area is 1/4 the area of the outer circle, πr² = 3 and r = √(3/π)
AO is the Radius of the outer circle and OD is the radius of the inner circle.
A line tangent to a circle and a radius drawn to the point of tangency form a right angle.
Thus, ∆AOD is a right triangle.
Hypotenuse AO is twice the length of leg OD.
A right triangle whose hypotenuse is twice the length of a leg is a 30-60-90 triangle.
Thus, ∆AOD is a 30-60-90 triangle.
In a 30-60-90 triangle, the sides are proportioned x : x√3 : 2x.
Thus, AD = √3 * √(3/π) * = 3/√π.
Using the same reasoning for ∆OCD, we can deduce that CD = 3/√π.
Thus, AC = 2 * 3/√π = 6/√π.
The formula for the area of an equilateral triangle = (s²√3)/4.
Since AC = 6/√π, the area of ∆ABC = (6/√π)² * √3/4 = 36/π * √3/4 = (9√3)/π.
Answer : C
Answer: C
Question: Capacity of a cylindrical vessel is 25,872 litres. If the height of the cylinder is 200% more than the radius of its base, what is the area of the base in square cms?
Options:
A)336
B)1232
C)616
D)926
E)cannot be determined
Rationale: let r be the radius
so height,h=r+(200% of r)=r+2r=3r
volume of cylinder=pi*r^2*h
or pi*r^2*3r=25872
or 22/7 *r^3=8624
or r^3=392*7=8*7*7*7
0r r=14
so area of base=22/7 *14*14=616
ANSWER:C
Answer: C
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Answer: C
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Options:
A)22 1/7
B)22 1/4
C)22 1/2
D)22 1/1
E)22 1/3
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 22 1/2 kmp Answer: C
Answer: C
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $9.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
Options:
A)$4.50
B)$5.10
C)$9.30
D)$5.50
E)$5.60
Rationale: I Tried using Time/Rate approach:-
Initial Price Difference = 9.80 - 3.20 = 6.60
Price of Corn increasing by 5x
Price of Wheat decreasing by x(1.4)-x = .4x
Since both the quantities are moving towards reducing the Price Gap hence:-
Relative Increase = 5x +.4x
Let T be the Time by which GAP is filled so,
6.6 = T(5.4x) -> T= (6.6)/5.4X
Final Price = 3.20 + 5X * T -> 3.20 + 5*6.6/5.4 = 9.3
Answer C.
Answer: C
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
Options:
A)10.27 a.m
B)10.15 a.m
C)10.27 a.m
D)10.55 a.m
E)10.25 a.m
Rationale: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Answer: E
Answer: E
Question: The marks obtained by Vijay and Amith are in the ratio 4:7 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
Options:
A)6:8
B)6:1
C)6:5
D)6:7
E)6:3
Rationale: 4:7
3:2
-------
12:21:14
12:14
6:7
Answer: D
Answer: D
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $791,000 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
Options:
A) $500,000
B) $448,000
C) $406,000
D) $313,600
E) $116,000
Rationale: My take is A.
(791000*4 + 112000*3)/7 = 500000
Answer: A
Question: A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold?
Options:
A)24
B)8
C)12
D)4
E)2
Rationale: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.
To solve, we have 2 equations and 2 unknowns
Let x = number of $3 Frisbees sold
Let y = number of $4 Frisbees sold
x + y = 64
3x + 4y = 200
x = 64 - y
3(64-y) + 4y = 200
192 - 3y + 4y = 200
y = 8
Answer: B
Answer: B
Question: If x is an integer and 2.13 × 10^x is less than 2100, what is the greatest possible value for x?
Options:
A)2
B)6
C)5
D)4
E)3
Rationale: If x=3
2.13 × 10^3 = 2130 > 2,100
So, x = 2
Answer : A
Answer: A
Question: k = 2^n + 8, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
Options:
A)2^n - 8
B)2^n - 2
C)2^n
D)2^n + 4
E)2^n + 5
Rationale: Given: k, M and N are integers
If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)
We're told that 9 is a divisor of 2^n + 8
We also know that 9 is a divisor of9.
So, applying the above rule, 9 is a divisor of 2^n + 8 +9, and 9 is a divisor of 2^n + 8 -9=2^n -1
D
Answer: D
Question: How many positive integers less than 30 have no common prime factor with 30?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: 30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Answer: D
Question: Derek throws three dice in a special game. If he knows that he needs 15 or higher in this throw to win, then find the chance of his winning the game.
Options:
A)5/54
B)13/115
C)20/145
D)6/54
E)90/155
Rationale: Total cases = 6*6*6
= 216
n(X)/n(S)
=20/216 = > 5/54
ANSWER A
Answer: A
Question: A person travelled from his house to office at 30km/hr and office to house at 70km/hr. Then find the average speed?
Options:
A)30km/hr
B)40km/hr
C)42km/hr
D)50km/hr
E)62km/hr
Rationale: Average speed = (2*30*70)/(30+70)= 42km/hrAnswer is C
Answer: C
Question: The mass of 1 cubic meter of a substance is 200 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 200 kg - 1 cubic meter;
200,000 g - 1 cubic meter;
200,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/200,000 = 10/2 = 5 cubic centimeters.
Answer: E.
Answer: E
Question: What fraction is equivalent to 0.8% ?
Options:
A)1/125
B)1/129
C)1/121
D)1/122
E)1/124
Rationale: Explanation:
0.8% = 0.8/100 = 8/1000 = 4/500 = 2/250 = 1/125
ANSWER: A
Answer: A
Question: A basketball is dropped from a height of 30 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces.
Options:
A)50
B)82.5
C)60
D)75
E)80
Rationale: Initial distance = 30 feet
first bounce = 15 feet up + 15 feet down = 30 feet
second bouche = 7.5 feet up + 7.5 feet down = 15 feet
third bounce = 375 feet up and 3.75 feet down= 7.5 feet
total distance covered = 30+30+15+7.5 = 82.5
ANSWER IS B
Answer: B
Question: The product of three consecutive numbers is 990. Then the sum of the smallest two numbers is ?
Options:
A)11
B)15
C)19
D)38
E)56
Rationale: Product of three numbers = 990
990 = 9*10*11.
So, the three numbers are 9, 10 and 11.
And Sum of smallest of these two = 9+10 = 19.
ANSWER : OPTION C
Answer: C
Question: During a certain season, a team won 75 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?
Options:
A)180
B)170
C)156
D)150
E)125
Rationale: We are first given that a team won 75 percent of its first 100 games. This means the team won 0.75 x 100 = 75 games out of its first 100 games.
We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:
0.5(T – 100) = number of wins for remaining games
0.5T – 50 = number of wins for remaining games
Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:
Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season
75 + 0.5T – 50 = 0.7T
25 = 0.2T
250 = 2T
125 = T
Answer is E.
Answer: E
Question: Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64},
II. {10, 16, 26, 42, 68},
III. {46, 59, 67, 72, 75}
Options:
A)I only
B)I & II
C)I & III
D)II & III
E)I, II, & III
Rationale: Original set: Q = {5, 8, 13, 21, 34}.
Notice that Set I is just every number in Q plus 30. When you add the same number to every number in a set, you simply shift it up without changing the spacing, so this doesn’t change the standard deviation at all. Set I has the same standard deviation as Q.
Notice that Set II is just every number in Q multiplied by 2. Multiplying by a number does change the spacing, so this does change the standard deviation. Set II does not have the same standard deviation as Q.
This one is very tricky, and probably is at the outer limit of what the GMAT could ever expect you to see. The spacing between the numbers in Set III, from right to left, is the same as the spacing between the numbers in Q from left to right. Another way to say that is: every number in Set III is a number in Q subtracted from 80. Again, would be very hard to “notice”, but once you see that, of course adding and subtraction the same number doesn’t change the standard deviation. Set III has the same standard deviation.
The correct combination is I and III, so the answer is C.
Answer: C
Question: A train speeds past a pole in 10 seconds and a platform 100 m long in 30 seconds. Its length is?
Options:
A)188 m
B)876 m
C)251 m
D)50 m
E)45 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 10 => y = x/10
x + 100 / 30 = x / 10
x = 50 m.
Answer: D
Answer: D
Question: The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
Options:
A)6
B)4
C)5
D)3
E)1
Rationale: P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
Answer: B
Answer: B
Question: In how many ways a committee consisting of 4 men and 2 women can be formed from 7 men and 3 women?
Options:
A)A)105
B)B)15
C)C)20
D)D)18
E)E)21
Rationale: Required number of ways = 7C4*3C2 = 35*3 = 105
Answer is A
Answer: A
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options:
A)20
B)80
C)100
D)200
E)220
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: Option C
Answer: C
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 500 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
A)340
B)346
C)352
D)365
E)370
Rationale: Number of newborns that can die in first month = 1/10 * 500 = 50
Survived = 450
Number of newborns that can die in second month = 1/10 * 450 = 45
Survived = 405
Number of newborns that can die in third month = 1/10 * 405 = 40
Survived = 365
Answer:D
Answer: D
Question: 90, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3
Options:
A)100
B)150
C)180
D)200
E)220
Rationale: 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
50*4=200
3*50=150 ans is 150
ANSWER:B
Answer: B
Question: In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Options:
A)A)0.9
B)B)0.6
C)C)0.45
D)D)0.3
E)E)0.25
Rationale: Percent of students who are 25 years old or older is 0.4*48+0.4*52=40, so percent of people who are less than 25 years old is 100-40=60.
Answer: B.
Answer: B
Question: If a number p is prime, and 2p+5= q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
Options:
A)1
B)2
C)5
D)7
E)9
Rationale: 2/9 = 0.2222222222222.. (a repeating pattern one digit long)
B
Answer: B
Question: A worker can load one truck in 6 hours. A second worker can load the same truck in 5 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill one truck?
Options:
A)2.7
B)2.9
C)3.1
D)3.3
E)3.5
Rationale: The workers fill the truck at a rate of 1/6 + 1/5 = 11/30 of the truck per hour.
Then the time to fill one truck is 30/11 which is about 2.7 hours.
The answer is A.
Answer: A
Question: Which of the following equivalent to (1/27)^2?
Options:
A)(0.10)^3
B)(0.11)^3
C)(0.12)^3
D)(0.13)^3
E)(0.14)^3
Rationale: (1/27)^2 = (1/3^3)^2 = (1/3)^6 = (1/9)^3 = (0.11)^3
Answer: Option B
Answer: B