divelab/Sys2Bench huggingface dataset:
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)877 m
B)240 m
C)167 m
D)887 m
E)265 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15
==> x + 300 = 540 ==> x
= 240 m.
Answer: B
Answer: B
Question: Walking at the rate of 8kmph a man cover certain distance in 4hr 45min. Running at a speed of 19 kmph the man will cover the same distance in.
Options:
A)100 min
B)110 min
C)140 min
D)120 min
E)150 min
Rationale: Distance = Speed * time
8*19/4= 38km
New Speed = 19kmph
Therefore time = D/S = 38/19= 120 min
Answer : D.
Answer: D
Question: A palindrome is a number that reads the same forward and backward, such as 464. How many odd five-digit numbers are palindromes?
Options:
A)40
B)400
C)500
D)5,000
E)100,000
Rationale: 5th digit 1,3,5,7,9
4th digit 0 through 9
3rd digit 0 through 9
i.e 10*10*5 = 500 numbers
first and second digit is going to be same as 4th and 5th. so it would still be 400 numbers.
Answer is C.
Answer: C
Question: A real estate investor decided to sell five of his apartments at the cost of $168,000, $235,000, $157,000, $ 256,000 and $ 235,000. Due to a bidding war, the price on the most expensive apartment will likely be sold for $15,000 higher than the initial asking price. Which of the following best describes how the mean and median would change as a result of a higher sale price on the most expensive apartment?
Options:
A)Both the mean and median will be unchanged.
B)The median will change but the mean remains unchanged.
C)The median will remain the same but the mean will increase.
D)Both the mean and the median will increase by the same percentage.
E)Both the mean and the median will increase by different amounts.
Rationale: Soln:
(C) The median will remain the same but the mean will increase.
ANSWER:C
Answer: C
Question: If [[x]] = x^2 + 2x + 4, what is the value of [[4]]?
Options:
A)3
B)9
C)15
D)19
E)28
Rationale: [[x]] = x^2 + 2x + 4
[[4]] = 4^2 + 2*4 + 4 = 28. Option E
Answer: E
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?
Options:
A)13
B)14
C)12
D)16
E)17
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Answer: C
Question: A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
Options:
A)4/5
B)1/3
C)2/4
D)1/5
E)2/6
Rationale: Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by
(number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3
correct answer B
Answer: B
Question: It takes one machine 3 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
Options:
A)a) 7/12
B)b) 1 1/2
C)c) 1 5/7
D)d) 3 1/2
E)e) 1 1/2
Rationale: RT = W
Given:
R = 1/3 + 1/3 = 2/3
T = ?
W = 1
T = 1 / (2/3) = 3/2 = 1 1/2
Answer: E
Answer: E
Question: There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
Options:
A)144
B)180
C)192
D)360
E)None of these
Rationale: Task 1 can not be assigned to either person 1 or 2 i.e.there are 4 options.
Task 2 can be assigned to 3 or 4
So, there are only 2 options for task 2.
So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6.
= 2 × 3 × 4 × 3 × 2 × 1 = 144
Answer A
Answer: A
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Options:
A)29.98
B)20.98
C)20.92
D)20.96
E)20.91
Rationale: 81 ---- 17
100 ----- ? è 20.98%loss
Answer:B
Answer: B
Question: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x
II. y/7 is an integer
III. The cube root of x is not necessarily an integer
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: Statement 1: y>x
When y=x=0, equation holds but y is not greater than x
When x=-8 and y=-91, equation again holds but x>y
NOT TRUE
Statement 2: y/7 is an integer
Since x and y are integers, 91x and 8y must also be integers.
It is given that 91x=8y
or 13*7*x = 8 y
or 13x = 8y/7
To balance the equation, y/7 must be an integer
TRUE
Statement 3: The cube root of x is an integer
x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3
So, x may or may not be a cube root.
TRUE
Answer:-E
Answer: E
Question: A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?
Options:
A)9%
B)10%
C)105/8%
D)11%
E)12%
Rationale: The equation we can form the question :
Return on Total Investment = Sum of individual Investments
(500+1500)(8.5)=(500∗7)+(1500x), where x is the return on investment of 1500.
Solving the equation, we get x = 9% ( Option A )	ANSWER:A
Answer: A
Question: How much interest can a person get on Rs. 8800 at 17.5% p.a. simple interest for a period of two years and six months?
Options:
A)3587.58
B)3587.59
C)3587.5
D)3587.52
E)3850
Rationale: I = (8800 * 2.5 * 17.5)/100 = (8800 * 5 * 35)/(100 * 2 * 2) = Rs. 3850.Answer: E
Answer: E
Question: A box contains 4 blue marbles, 3 red, 6 green marbles and two yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)5/10
B)4/10
C)1/10
D)2/10
E)3/10
Rationale: Given that there are 4 blue marbles, 3 red marbles, 6 green marbles and 2 yellow marbles. Probability that both marbles are blue = 4Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 2/35
Probability that both are yellow = Â²Câ‚‚/Â¹âµCâ‚‚ = (1)/(15 * 14) = 1/210
Probability that one blue and other is yellow = (4Câ‚ * Â²Câ‚)/Â¹âµCâ‚‚ = (4*2)/(15 * 14) = 4/105
Required probability = 2/35 + 1/210 + 4/105
= 1/10
Answer:C
Answer: C
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 37. Find the third number?
Options:
A)A)37
B)B)85
C)C)48
D)D)43
E)E)84
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 37
6x = 48 => third number is 37.
Answer: Option A
Answer: A
Question: A person has to cover a distance of 6km in 45 minutes. If he covers one half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed must be?
Options:
A)12km per hr
B)10km/hr
C)15km/hr
D)20km/hr
E)18km/hr
Rationale: Remaining distance = 3km
Remaining time = 1/3 * 45 = 15min = 1/4 hour
Required speed = 3*4 = 12km/hr
Answer is A
Answer: A
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
Options:
A)4 3/9 km
B)5 3/8 km
C)4 3/8 km
D)6 3/8 km
E)7 3/8 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8 = 4 3/8 km
Answer:C
Answer: C
Question: What amount does an investor receive if the investor invests $7000 at 10% p.a. compound interest for two years, compounding done annually?
Options:
A)$8080
B)$8130
C)$8260
D)$8320
E)$8470
Rationale: A = (1 + R/100)^n * P
(1.1)^2 * 7000 = 1.21 * 7000 = 8470
The answer is E.
Answer: E
Question: If 16 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?
Options:
A)127
B)225
C)287
D)450
E)281
Rationale: Explanation:
Let the required no of hectares be x. Then
Men --- Hectares---Days
16---------80---------24
36---------x---------30
More men, More hectares (Direct proportion)
More days, More hectares (Direct proportion)
x=36/16*30/24*80
x= 225
Answer: B
Answer: B
Question: If p is a positive integer, and r is the units digit of 3^4p×5^5p×6^6p×7^7p then r + 2 is divisible by which of the following?
Options:
A)2
B)3
C)5
D)7
E)9
Rationale: The number will be an even number as it contains 6 as a term in its product, so units digit will be even..
EVEN +2 will be another EVEN and will be div by 2..
ANSWER:A
Answer: A
Question: A reduction of 18% in the price of oil enables a house wife to obtain 8kgs more for Rs.1080, what is the reduced price for kg?
Options:
A)72.15
B)27.24
C)24.25
D)28.46
E)20.9
Rationale: 1080*(18/100) = 194 ---- 8
? ---- 1 => Rs.24.25
Answer:C
Answer: C
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)Rs.2(1/9)
B)Rs.2(2/9)
C)Rs.3(1/9)
D)Rs.1(1/9)
E)Rs.2(2/5)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs.2(2/9)
B
Answer: B
Question: A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?
Options:
A)$31.63
B)$35.63
C)$32.63
D)$37.63
E)$33.63
Rationale: A
$31.63
The amount must have been $31.63. He received $63.31. After he had spent a nickel there would remain the sum of $63.26, which is twice the amount of the check.
Answer: A
Question: Lorna invests $7000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
Options:
A)$160
B)$1,600
C)$2,200
D)$1,400
E)$5,840
Rationale: We have that 'x' invested at 6%
We also have that '6000-x' invested at 11%
Now then 580/7000 is approx 10%
Therefore, -4x+7000-x=0
5x=7000
x=1400 approximately. Probably higher
Only D matches
Answer: D
Question: By travelling at 70 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Options:
A)25 kmph
B)20 kmph
C)28 kmph
D)35 kmph
E)32 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance = 70 * 3x = 210x km
He covered 2/3 * 210x = 140x km in 1/3 * 3x = x hours So, the remaining 70x km, he has to cover in 2x hours. Required speed = 70x/2x
=35 kmph.
Answer: D
Answer: D
Question: The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 50% profit?
Options:
A)$480
B)$450
C)$960
D)$870
E)$660
Rationale: C
$ 960
Let C.P. = $ x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of $ 640 = 150/100 * 640 = $ 960.
Answer: C
Question: Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
Options:
A)5040
B)2520
C)720
D)120
E)42
Rationale: 7! = 5040
5040/2=2520 half the time carmelo is in front, vice versa
Answer:
(B) 2520
Answer: B
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 32, the how old is B?
Options:
A)7
B)9
C)8
D)11
E)12
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 32
⇒ 5x = 30
⇒ x = 6.
Hence, B's age = 2x = 12 years.
Answer: E
Answer: E
Question: Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of
Rs. 13,800. Deepak's share is
Options:
A)Rs 9600
B)Rs 8500
C)Rs 8450
D)Rs 8400
E)None of these
Rationale: Explanation:
Ratio of their shares	= 22500 : 35000
=9 : 14
Deepak's share	= Rs.(13800×14/23)
= Rs. 8400
Option D
Answer: D
Question: A man performs 1/2 of his journey by rail, 2/5 by bus and the remaining 10 km on foot. His total journey is?
Options:
A)40km
B)50km
C)60km
D)70km
E)100km
Rationale: Let the total journey be x km
x/2 + 2x/5 + 10 = x
9x+50 = 10x
x = 50 km
Answer is B
Answer: B
Question: A straight pipe 1 yard in length was marked off in fourths and also in fifths. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
Options:
A) 1/6 and 1/4 only
B) 1/4 and 1/3 only
C) 3/20, 1/5 and 1/10
D) 1/12, 1/6 and 1/4
E) 1/20, 3/20, 1/5 and 1/10
Rationale: Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4
and 5th : 0/5, 1/5, 2/5, 3/5 , 4/5, 5/5
Now with understood common denominator 20 write the numbers : for 4th : 0,5,10,15,20 and for 5th : 0,4,8,12,16,20
Now comine : 0,4,5,8,10,12,15,16,20
Now find the cut with denominator 20 (Substracrt adjacent terms : 1/5, 1/20, 3/20, 1/10,1/10,3/20,1/20,1/5 i.e. 1/5, 1/20 ,3/20 and 1/10 after removing duplicates.
Answer : E
Answer: E
Question: If n is a positive integer, which of the following expressions must be even?
Options:
A)(n − 3)( n + 1)
B)(n − 8)( n + 1)
C)(n − 4)( n + 4)
D)(n − 5)( n + 1)
E)(n − 5)( n + 5)
Rationale: Whether n is even or odd, (n-8)(n+1) will have one odd factor and one even factor.
The product will be even.
The answer is B.
Answer: B
Question: The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. The age of the youngest boy is:
Options:
A)21 years
B)18 years
C)15 years
D)9 years
E)None of these
Rationale: Total age of 3 boys = (25 × 3) years = 75 years. Ratio of their ages = 3 : 5 : 7.
Age of the youngest = (75 × 3⁄15) years = 15 years.
Answer C
Answer: C
Question: List I: { y, 2, 4, 7, 10, 11}
List II: {3, 3, 4, 6, 7, 10}
If the median T of List I is equal to the sum of the median of list II and the mode of list II, then y equals
Options:
A)5
B)7
C)8
D)T=9
E)10
Rationale: mode of list ii =3
median T of list ii =4+6/2 =5
sum of mode + mean = 3+ 5=8
now to make 8 as the median we need to find a value of y such that if the no. of terms in list 1 are odd then y=8 else if even then 7+y /2=8
here its even so
7+y/2=8 from this y= 9 (D)
Answer: D
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 27,000 is made?
Options:
A)Rs. 1,10,000
B)Rs. 1,23,000
C)Rs. 1,24,000
D)Rs. 1,21,000
E)None of these
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 27,000 = Rs. 1,23,000
ANSWER:B
Answer: B
Question: If two integers x,y (x>y) are selected from -5 to 6 (inclusive), how many cases are there?
Options:
A)62
B)66
C)70
D)74
E)78
Rationale: There are 12 integers from -5 to 6 inclusive.
12C2 = 66.
The answer is B.
Answer: B
Question: Six animals of a circus has to be placed inside in six cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
Options:
A)A.240
B)B.808250
C)C.502450
D)D.784200
E)E.302400
Rationale: ways for cages that are too small = 5*4*3*2=120
since we have 2 cages and 2 animal left therefore ways for 2 cages =2!
total ways =120*2!=604800
Answer A
Answer: A
Question: How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?
Options:
Options:
A)ONE
B)TWO
C)THREE
D)FOUR
E)FIVE
Rationale: Numbers giving remainder 3 when divided by 10 = 13,23, 33,43, 53,63, 73,83, 93
Numbers giving remainder 3 when divided by 4 = Alternate numbers (coloured in red) = 4
Correct Option:	D
Answer: D
Question: In a class there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row there are 2 more desks than in the previous row. Find the maximum number of students seated in the class?
Options:
A)112
B)144
C)136
D)132
E)118
Rationale: The 8 rows form an Arithmetic progression with first term 10 and last 24. Avg is 17.
so 17*8=136
Answer is C.
Answer: C
Question: In how many ways can the letters of word CREMATION be arranged such that NO two vowels appear together?
Options:
A)9!
B)5!*4!
C)4!*5!
D)5!*4!*2!
E)6!*4!
Rationale: No 2 vowels together = the only arrangement possible will be C V C V C V C V (with V=vowel, C=consonant). This is true as we have 4 vowels and 5 consonants and any other combination will force us to pair 2 vowels together.
Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 4!*5! ----> C is the correct answer.
Answer: C
Question: A factory produces 4560 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Options:
A)1140 toys
B)2375 toys
C)3375 toys
D)4375 toys
E)5375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
4560 / 4 = 1140 toys
correct answer A
Answer: A
Question: A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
Options:
A)Rs. 460
B)Rs. 484
C)Rs. 550
D)Rs. 664
E)none
Rationale: (4/15)A = (2/5)B
A = (2/5 * 15/4)B
A = (3/2)B
(A/B) = (3/2)
A : B = 3: 2
B's share = Rs. (1210 * 2/5) = Rs. 484
Answer = B
Answer: B
Question: Train starts from amritsar to Bombay at 9am. It reaches destination after 3days at 9:30am. Every day a train starts. How many trains does it come across on the way ?
Options:
A)5th
B)4th
C)6th
D)7th
E)8th
Rationale: because one train taking 3 days
so 1 train first day
another at second day
and 3rd one at third day
but as given train reaches at 9.30 am insted of 9.oo am
so d same day train already left
that train will be 4th train.
ANSWER:B
Answer: B
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 60 units raises the average to 55 units per day, what is the value of n ?
Options:
A)30
B)18
C)10
D)9
E)1
Rationale: (average production for n days) * n = (total production for n days) --> 50n=(total production for n days);
(total production for n days) + 60 = (average production for n+1 days) * (n+1) --> 50n + 60 = 55 * (n+1) --> n=1.
Answer: E.
Answer: E
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
Options:
A)26%
B)25%
C)15%
D)28%
E)55%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer:B
Answer: B
Question: There were two candidates in an election. Winner candidate received 56% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
Options:
A)776
B)1344
C)299
D)257
E)125
Rationale: W = 56% L = 44%
56% - 44% = 12%
12% -------- 288
56% -------- ? => 1344
Answer:B
Answer: B
Question: Rahul went to purchase a Nokia mobile handset, the shopkeeper told him to pay 20% tax if he asked the bill. Rahul manages to get the discount of 5% on the actual saleprice of the mobile and he paid the shopkeeper Rs. 3325 without tax. Besides he manages to avoid to pay 20% tax on the already discounted price, what is the amount of discount that he has gotten?
Options:
A)750
B)375
C)875
D)525
E)625
Rationale: Explanation:
CP = 100, SP (with tax) =120
New SP = 100 - 5 = 95
\therefore Effective discount = 120 - 95 = 25
So, at SP of 95 ----> discount = 25
and at SP of 3325 -----> discount = 25/95=3325=875.
Answer: C
Answer: C
Question: A 2-year certificate of deposit is purchased for E dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
Options:
A)k(1.06)^2
B)k(1.06)^8
C)k(1.015)^2
D)E(1.015)^8
E)k(1.03)^4
Rationale: Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%
Now, periods of compounding in 2 years= 8 (8 quarters)
Thus E(1.015)^8
Answer: D
Answer: D
Question: Farm Tax is levied on the 50% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
Options:
A)15%
B)25%
C)0.125%
D)0.2083%
E)none
Rationale: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/50) = 25%
The correct answer is (B).
Answer: B
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.15 km and 0.6 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)42
B)9
C)7
D)67
E)15
Rationale: :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.15 + 0.6 = 1.75 km = 1750 m.
Required time = 1750 * 3/125
= 42 sec.
Answer: A
Answer: A
Question: In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Options:
A)69.
B)73.
C)81
D)91
E)108
Rationale: Total students = 420
Boys = 312, Girls = 108
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 108 - 35 = 73.
Correct option: B
Answer: B
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?
Options:
A)9%
B)10%
C)11%
D)12%
E)15%
Rationale: x discount on Pony jeans, (0.22 - x) discount on Fox jeans.
Set the equation: 3*15(0.22 - x) + 2*18x = 9 --> x = 0.1 = 10%.
Answer: B.
Answer: B
Question: 4^15 is equal to which of the following?
Options:
A)1,073,751,828
B)1,073,751,824
C)1,073,751,842
D)1,073,751,806
E)1,073,751,821
Rationale: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 4^n has a cycle of 1.
4^1 = 4
4^2 = 16
4^3 = 64
Observe that the last digit of the resultant of 4^1 and 4^3 is 4. If we continue 4^n, the last digit follows the pattern 4, 6, 4, 6, 4, 6, .... So, all we need look for is the last digit in the pattern.
Cycle of 1, power of 15, last digit is 4.
Answer: B
Answer: B
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $468 per week. How much does she earn in dollars per hour?
Options:
A)2
B)8
C)9
D)11
E)13
Rationale: Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 468. Hourly wage = 468 / 36 = 13
Answer: E
Answer: E