mathewhe/aqua_rat huggingface dataset:
Question: A test has 160 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?
(A) 23
(B) 25
(C) 27
(D) 29
(E) 31
Rationale: A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.
Let C be the number of correct answers and let I be the number of incorrect answers.
To get 40 points, a test taker must have at least 40 correct answers. Then C=> 40.
For every correct question above 40, the test taker has 4 incorrect answers.
Then, the I = 4*(C - 40).
Also, I + C <= 160. Thus 5C <= 320 and so C <= 64.
Then 40 <= C <= 64 and C can have 25 possible values.
The answer is B.
Answer: (B) 25
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 1 to 7 to 8. If a total of 80 sandwiches were made, how many bologna sandwiches
were made?
(A) 15
(B) 30
(C) 35
(D) 42
(E) 48
Rationale: For deciding such task we should calculate all parts 1 + 7 + 8 = 16 parts
and we should calculate how many sandwiches holds 1 part:
80 / 16 = 5 sandwiches in one part
For bologna we have 7 parts so:
7 * 5 = 35
Answer is C
Answer: (C) 35
Question: In a class,12 students like to play Basketball and 8 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
(A) 12
(B) 15
(C) 17
(D) 18
(E) 22
Rationale: Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
12 +8 - 3 = 17
C)
Answer: (C) 17
Question: A patient was given three pills which he is required to take one after every thirty-five minutes.
How long can the pills run for him?
(A) 1 hour and 10 minutes.
(B) 1 hour and 15 minutes.
(C) 1 hour and 20 minutes.
(D) 1 hour and 50 minutes.
(E) 1 hour and 25 minutes.
Rationale: He took the first pill at the zero minute.
He took the second pill after 20 minutes = 0+35=35
He took the third pill after 20 minutes = 35+35=70
Then it will last for 70 minutes or an hour and 10 minutes.
Answer A
Answer: (A) 1 hour and 10 minutes.
Question: A family pays $800 per year for an insurance plan that pays 65 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.
(A) $1,000
(B) $1,200
(C) $1,400
(D) $1,500
(E) $2,200
Rationale: Upfront payment for insurance plan = 800$
Family needs to pay 35 % of first 1000 $ in expense = 350$
Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 350 = 1150 $
Total amount paid by insurance plan for first 1000 $ = 800 $
Total amount paid by family will equal amount paid by plan when medical expense = 1500 $
(Since insurance plan will pay 100% of amount that exceeds 1150$ )
Answer D
Answer: (D) $1,500
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 900 km
(B) 800 km
(C) 600 km
(D) 690 km
(E) 609 km
Rationale: Explanation:
D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km
Answer: Option C
Answer: (C) 600 km
Question: A car moves at 92 km/hr. What is the speed of the car in meters per second ?
(A) 20 2/9m sec
(B) 22 2/9m sec
(C) 25 5/9m sec
(D) 26 2/9m sec
(E) 28 2/9m sec
Rationale: Explanation:
Speed=(92∗5/18)m/sec
=230/9 m/sec
=25 5/9msec
Option C
Answer: (C) 25 5/9m sec
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 46 percent were employees. What percent were stockholders, who were not employees?
(A) 52
(B) 54
(C) 59
(D) 55
(E) 56
Rationale: I came up with the same answer choice B, but my approach was slightly different!
46% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 46% = 54%.
Answer: (B) 54
Question: The C.P of 14 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 16 2/8% loss
(C) 16 3/3% loss
(D) 22 2/9% loss
(E) 56 2/3% loss
Rationale: 14 CP = 18 SP
18 --- 4 CP loss
100 --- ? => 22 2/9% loss
Answer:D
Answer: (D) 22 2/9% loss
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres?
(A) 20
(B) 200
(C) 300
(D) 90
(E) 140
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 8480
[4L - 40] = 8480 / 26.50 = 320
4L = 360
L = 360/4= 90 meters. Answer: D
Answer: (D) 90
Question: If 10^(x-1)< 0.000125 <10^x, what is the value of an integer x?
(A) -4
(B) -3
(C) -2
(D) 3
(E) 4
Rationale: -> Multiply 10^6- > (10^6){10^(x-1)}<125<(10^6)(10^x) -> 125 is bigger than 100
-> (10^6)(10^(x-1))=100 -> 10^(6+x-1)=10^2, x+5=2 -> x=-3
Thus, the answer is B
Answer: (B) -3
Question: Of 90 applicants for a job, 42 had at least 4 years' experience, 54 had degrees, and 8 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 10
(B) 8
(C) 14
(D) 16
(E) 12
Rationale: 90 - 8 = 82
82 - 42 - 54 = -14
Then 14 are in the intersection between 4 years experience and degree.
Answer : C
Answer: (C) 14
Question: What number is obtained by adding the units digits of 734^99 and 347^83?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: The units digit of 734^99 is 4 because 4 raised to the power of an odd integer ends in 4.
The units digit of 347^83 is 3 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 83 is in the form 4n+3, the units digit is 3.
Then 4+3 = 7.
The answer is A.
Answer: (A) 7
Question: A man has Rs. 512 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 80
(B) 90
(C) 96
(D) 98
(E) 100
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 512
16x = 512
x = 32.
Hence, total number of notes = 3x = 96.
C
Answer: (C) 96
Question: A study group consists of 4 English majors, 6 biological sciences majors, and 5 engineers. In how many ways can 3 English majors, 3 biological science majors and 3 engineers selected from the given group?
(A) 987 ways
(B) 346 ways
(C) 600 ways
(D) 200 ways
(E) 134 ways
Rationale: The number of ways of selecting three English majors, two biological science majors and three engineers is:
= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(3 * 2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 5 * 10
= 200 ways.
Answer: D
Answer: (D) 200 ways
Question: If the range T of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 	0
(B) 	2
(C) 	12
(D) 	13
(E) 	15
Rationale: The range T of a set is the difference between the largest and smallest elements of a set.
Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.
The the difference between the greatest possible value of x and least possible value of x is 15-2=13.
Answer: D.
Answer: (D) 	13
Question: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the five interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
(A) 25
(B) 81
(C) 90
(D) 10!/2!
(E) 10!
Rationale: I lined up the 10 different colours for Exterion and Interior like this:
E: A B C D E F G H I J
I: A B C D E F G H I J
I calculated the number of combinations: 10*10= 100 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 25.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
A
Answer: (A) 25
Question: In a soccer bet,we play 4 teams.first team odd 1.25,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
(A) 217.78
(B) 225.5
(C) 235.01
(D) 266.74
(E) 669.0
Rationale: in the case we won the bet,we have:
1.25* 5.23* 3.25* 2.0*5.00=219.50
we will win 217.78
so correct answer is A
Answer: (A) 217.78
Question: 36 men can complete a piece of work in 18 days. In how many days will 81 men complete the same work ?
(A) 8
(B) 77
(C) 88
(D) 29
(E) 21
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
81 : 36 :: 18 : x
x = 8
Answer: A) 8 days
Answer: (A) 8
Question: If the average (arithmetic mean) of 16 consecutive odd integers is 414, then the least of these integers is
(A) a) 399
(B) b) 418
(C) c) 519
(D) d) 521
(E) e) 525
Rationale: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 16 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 7th and 8th numbers in the set). This means that numbers 7 and 8 in this set are 413 and 415. Because we know that number 7 is 413, we know that the smallest number is 7 odd numbers below this, which means that it is 7*2 = 14 below this (every odd number is every other number). Therefore 413-14 = 399, answer choice A.
Answer: (A) a) 399
Question: A photography dealer ordered 30 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 30 cameras?
(A) 7% loss
(B) 13% loss
(C) 6% profit
(D) 13% profit
(E) 15% profit
Rationale: Total cost 30*($250/1.2)=6250;
# of cameras sold is 30-6=24 total revenue is 24*250;
# of cameras returned is 6 total refund 6*(250/1.2)*0.5;
So, total income 24*250+ 6*(250/1.2)*0.5
The dealer's approximate profit is (24*250+ 6*(250/1.2)*0.5-6250)/(6250)*100= 6%
Answer: C.
Answer: (C) 6% profit
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 980gm. for a kg.His gain is …%.
(A) 2.04%
(B) 5.36%
(C) 4.26%
(D) 6.26%
(E) 7.26%
Rationale: His percentage gain is 100*20/980 as he is gaining 20 units for his purchase of 980 units.
so 2.04%..ANSWER:A
Answer: (A) 2.04%
Question: A sum 's' is divided into 4 parts. second person gets Rs 10
more than first.3rd person is Rs 10 more than second,4th is 10 more than 3rd.how much amount do 1st person get.?
(A) x = (s-60)/4
(B) x = (s-60)/5
(C) x = (s-60)/3
(D) x = (s-60)/2
(E) x = (s-60)/6
Rationale: let x be amount getting by first person,
second person gets x +10,third person gets x + 20,fourth person gets x + 30,
now s = (x)+(x+10)+(x+20)+(x+30)
s = 4x + 60
s - 60 = 4x
or x = (s-60)/4
ANSWER:A
Answer: (A) x = (s-60)/4
Question: For each hour of production, a certain factory requires 1 assembly line worker for every 10 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 50N in one hour, where N is a positive integer?
(A) 12 + 5N
(B) 12 + 2N
(C) 62N
(D) 37N
(E) 25
Rationale: 10 units = 1 worker;
50N units = 50N/01 = 5N workers.
So, the answer is 5N workers plus 12 managers.
Answer: A.
Answer: (A) 12 + 5N
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 90 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 15 sec
(B) 19 sec
(C) 12 sec
(D) 10 sec
(E) 11.25 sec
Rationale: Explanation:
D = 250 m + 250 m = 500 m
RS = 90 + 70 = 160 * 5/18 = 400/9
T = 500 * 9/400 = 11.25 sec
Answer: Option E
Answer: (E) 11.25 sec
Question: In a chess tournament each of the six players will play with
every other player exactly once. How many matches will be
played during the tournament?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: if 2 players are playing thn no of match= 1
if 3 player are playing thn no of match =2
hence for Pth player no of matches = n-1 where n= no of players
so for 6th player it is 5
for 5th it is 4....
for 1 it is 0.
don't be confuse 1 already played with 6,5,4,3,2
__________________
6--->5,4,3,2,1
5----->4,3,2,1
4---->3,2,1
3---->2,1
2---->1
5+4+3+2+1=15
ANSWER:E
Answer: (E) 15
Question: A train is 360 meter long is running at a speed of 90 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 65 seconds
(B) 46 seconds
(C) 40 seconds
(D) 20 seconds
(E) 26 seconds
Rationale: Speed = 90 Km/hr = 90*(5/18) m/sec = 25 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/25)
= 20 seconds
Answer:D
Answer: (D) 20 seconds
Question: How many 7 in between 1 to 130?
(A) 18
(B) 20
(C) 22
(D) 23
(E) 24
Rationale: 7,17,27,37,47,57,67,
70,71,72,73,74,75,76,77(two 7's),78,79,87,97,107,117,127
23 7's between 1 to 130
ANSWER:D
Answer: (D) 23
Question: The median annual household income in a certain community of 21 households is $50,000. If the mean W income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years?
(A)  $50,000
(B)  $60,000
(C)  $60,500
(D)  $65,000
(E)  Cannot be determined
Rationale: Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean W is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.
Answer: (E)  Cannot be determined
Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
(A) 23
(B) 28
(C) 27
(D) 19
(E) 24
Rationale: Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64
= 16P => P
= 19.
Answer: D
Answer: (D) 19
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 2. If p is any prime number then f(p)=
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.
Answer: E.
Answer: (E) 2
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 6 muffins remained. How many guests did Monica plan on?
(A) 3.
(B) 4.
(C) 5.
(D) 6.
(E) 7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 6 = 5x + 2
6x - 6 = 5x + 2
x = 8
Answer: A
Answer: (A) 3.
Question: If the sides of a triangle are 26 cm, 24 cm and 20 cm, what is its area?
(A) 120
(B) 772
(C) 288
(D) 266
(E) 240
Rationale: The triangle with sides 26 cm, 24 cm and 20 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 20 = 240 cm2
Answer: E
Answer: (E) 240
Question: The total age of A and B is 10 years more than the total age of B and C. C is how many year younger than
(A) 14 years
(B) 12 years
(C) 56 years
(D) 10 years
(E) 55 years
Rationale: Given that A+B = 10 + B + C
=> A â€“ C = 10 + B â€“ B = 10
=> C is younger than A by 10 years
Answer:D
Answer: (D) 10 years
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 28 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
(A) 70
(B) 245
(C) 150
(D) 200
(E) 350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 28, so 0.14*{total} = 28 --> {total} = 200.
Answer: D.
Answer: (D) 200
Question: Tough and Tricky questions: Distance/Rate.
On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 200 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?
(A) 20
(B) 40
(C) 50
(D) 80
(E) 100
Rationale: Say, if speed is 40, 200/40 = 5 hrs and 200/50 = 4 hrs (a reduction of 1 hr -> Correct answer)
Answer (B)
Answer: (B) 40
Question: In how many ways can the letters of the word 'APPLE' be arranged?
(A) 48
(B) 60
(C) 56
(D) 32
(E) 18
Rationale: The word APPLE contains 5 letters
1A,2P,1L AND 1E
required number of ways = 5!/(1!*2!*1!*1!) = 60
Answer is B
Answer: (B) 60
Question: There are 400 tigers at a large zoo. The number of tigers is 5 times the number of all the other animals combined. How many more tigers are there than non tigers animals at the zoo?
(A) 400
(B) 390
(C) 370
(D) 320
(E) 90
Rationale: Answer is B.
Total tigers= 400 = 5 * Other Animals (X)
or X = 80.
So, Difference in tigers and X = 400-80 = 320.
Answer: (D) 320
Question: ? + 3699 + 1985 - 2047 = 31111
(A) 21274
(B) 27474
(C) 21224
(D) 27224
(E) None of these
Rationale: Explanation :
Let x + 3699 + 1985 - 2047 = 31111
=> x = 31111 - 3699 - 1985 + 2047 = 27474. Answer : Option B
Answer: (B) 27474
Question: If x^2 - 4 = 0 and x < 0, which of the following must be equal to 0 ?
(A)  x^2 - 9x
(B)  x^2 - 9x + 20
(C)  x^2 - 2x + 3
(D)  x^2 + 2x - 3
(E)  x^2 + 5x + 6
Rationale: x^2-4 = 0
x= +2 or x = -2
if we substitute x= -2 in the equation x^2 +5x+6 = 4-10+6 = 0
E is also the answer
Answer: (E)  x^2 + 5x + 6
Question: On Monday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
(A) Tuesday
(B) Wednesday
(C) Thursday
(D) Friday
(E) Saturday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Monday, 3rd day is Thursday. Next day, which he won't have a new combination for, is Friday. (D)
Answer: (D) Friday
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?
(A) 18%
(B) 20%
(C) 17%
(D) 18%
(E) None of these
Rationale: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.130.
SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117.
Gain = Rs.117 – Rs.100 = Rs.17
Therefore, gain/profit percent = 17%.
Answer: Option C
Answer: (C) 17%
Question: Certain sales in December were 50% less than they were in January and 50% greater than they were in Febuary. What was the percentage decrease in the stocks from January to February ?
(A) 70.1%
(B) 55%
(C) 66.7%
(D) 57.5%
(E) 45.8%
Rationale: Let stocks value in Feb = 100 => In Jan =50 and March = 50 * 100/150 = 33.3
Thus, percent decrease in stocks from Feb to March = 100 - 33.3 =66.7%
Hence Answer is C
Answer: (C) 66.7%
Question: A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1580 are infected, how manyworkersinhabit the colony?
(A) 1500
(B) 2500
(C) 2750
(D) 3000
(E) 3250
Rationale: From two question we get wo equations:
(1) 0,3s + 0,14w = 1580
(2) s + w = 7000
From (2) we get w=7000-s
In (1) 0,3s + 980-0,14s= 1580
0,16s=600
60000:16= 3750 =s
In (2) 3750 + w = 7000
w= 3250 E
Answer: (E) 3250
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 27, the how old is B?
(A) 7
(B) 9
(C) 8
(D) 11
(E) 10
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 = 27
⇒ 5x = 25
⇒ x = 5.
Hence, B's age = 2x = 10 years.
Answer: E
Answer: (E) 10
Question: A certain fruit stand sold jackfruit for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?
(A) 16
(B) 15
(C) 14
(D) 13
(E) 11
Rationale: Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.
63 is a direct multiple of 7, however in this case there won't be any bananas. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 .
E
Answer: (E) 11
Question: jeya travels the first 8 hours of her journey at 50 mph speed and the remaining 2 hours at 30mph speed. What is the average speed of jeya's travel in mph?
(A) 41mph
(B) 43mph
(C) 44mph
(D) 42mph
(E) 46mph
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by jeya= Distance covered in the first 8 hours + Distance covered in the next 2 hours.
Distance covered in the first 8 hours = 8Ã—50=400 miles
Distance covered in the next 2 hours= 2Ã—30=60 miles
Therefore, total distance travelled = 400+60=460 miles.
The total time taken = 8+2=10hours.
Hence, the average speed =460/10= 46mph.
Answer : E
Answer: (E) 46mph