mathewhe/aqua_rat huggingface dataset:
Question: The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 20 minutes after it was poured was how many degrees Fahrenheit?
(A) 65
(B) 75
(C) 80
(D) 85
(E) 90
Rationale: Answer: B
The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 20 minutes after it was poured is:
F = 120 ( 2 ^ -20/10) + 60
F = 120 * 1/ 4 + 60
F = 30 + 60
F = 90
E
Answer: (E) 90
Question: There are 13 South American countries, Anny has won a ticket to fly from Denver to one South American country and then directly to another South American Country before returning home to Denver again. Assuming there are four airports in each country, how many flights paths can Anny choose from?
(A) 13.12.11.10.4.4.
(B) 13.12.11.10.4
(C) 13.12.4.4.
(D) 13.12.4
(E) 13.13.13.13
Rationale: flights paths can Anny choose from There are 13 ways to chose the first destination,
then, 12 ways to chose next destination, with option of 4 airports (13x4)
then, to return he has 4 options to chose the airports
Thus, 13*12*4*4 ways.
Using permutations:
If the solution had written 13P1 instead of 13C1 it won't matter. As per the definition - making arrangements of the combinations gives permutations.
Since there are no arrangement for 1 item, permutationscombinations are equal.C
Answer: (C) 13.12.4.4.
Question: log4 2+log4 32 i equal to?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: apply log(ab) for each term
then log4+log2+log4+log32
2log2+log2+2log2+5log2 add these==>10log2=10*0.3=3
ANSWER:B
Answer: (B) 3
Question: If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 3m + n?
(A) 11
(B) 18
(C) 20
(D) 45
(E) 33
Rationale: k^4=5400∗mn
k^4=3^3.2^3.5^2.mn
In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2
mn=3.2.5^2
mn = 150 = 10 * 15 (Least possible)
Answer = 3*10 + 15 = 45
ANSWER:D
Answer: (D) 45
Question: Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 9, what is the measure of side XY?
(A) 4
(B) 4√2
(C) 8
(D) 6
(E) Cannot be determined from the information provided
Rationale: ans D..6..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=9 or yz=3*\sqrt{2}..
therefore hyp=xy=6
Answer: (D) 6
Question: A train 310 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 4
(B) 6
(C) 5
(D) 17
(E) 13
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [310 * 3/55] sec = 17 sec
ANSWER:D
Answer: (D) 17
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.40 m space around the room. A side of square tile is given to be 40 cms?
(A) 164
(B) 476
(C) 268
(D) 208
(E) 276
Rationale: Area of the room =3.2 * 8.2 =26.24
Area of the tile = 0.4 *0.4=0.16
No. of tiles =26.24/0.16 =164
Answer : A
Answer: (A) 164
Question: Let the number which when multiplied by 15 is increased by 196.
(A) 14
(B) 20
(C) 26
(D) 28
(E) 30
Rationale: Solution
Let the number be x .
Then, 15x - x = 196
‹=›14x = 196
x ‹=› 14.
Answer A
Answer: (A) 14
Question: There are 35 students in a hostel. If the no. of students increases by 8, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) 371.87
(B) 400.37
(C) 420.37
(D) 450.37
(E) 480.37
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 8) = x – 1
or, 35x + 42 = 43x – 43
or, x = 10.625
Thus the original expenditure of the mess = 35 x 10.625 = Rs. 371.87
A
Answer: (A) 371.87
Question: In a company, 52 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
(A) 65%
(B) 70%
(C) 75%
(D) 80%
(E) 85%
Rationale: The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
48% of all employees are women, so non-union women are 48%-18% = 30%
40% of all employees are non-union.
The percent of non-union employees who are women is 30%/40% = 75%
The answer is C.
Answer: (C) 75%
Question: The average of 28 numbers is 45. If two numbers namely 40 and 45 are discarded, The average of
remaining numbers is?
(A) 35.5
(B) 37.5
(C) 45.1
(D) 34.5
(E) 38.5
Rationale: Total of 50 numbers = 28 * 45 = 1260
Average of 26 numbers = 1260-(40+55) / 26
= 1175 / 26= 45.1
Answer is C.
Answer: (C) 45.1
Question: If the sales tax be reduced from 3 (1/5) % to 2 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 6400?
(A) Rs. 150.40
(B) Rs. 44.80
(C) Rs. 140.40
(D) Rs. 50.48
(E) None of these
Rationale: Explanation:
Required difference = (3 (1/5) of Rs. 6400) - (2 (1/2) of Rs. 6400)
= (16/5 – 5/2) % of Rs. 6400
= (7/10) x (1/100) x 6400
= Rs. 44.80
ANSWER B
Answer: (B) Rs. 44.80
Question: In how many ways the letters of the word RAIXBON be arranged?
(A) 4354
(B) 8454
(C) 4356
(D) 5040
(E) 6557
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
D)
Answer: (D) 5040
Question: Paul's salary was decreased by 50% and subsequently increased by
50%.How much percent does he lose?
(A) 0
(B) 25
(C) 50
(D) 30
(E) 40
Rationale: Let the original salary = $100
New final salary=150% of (50% of Rs.100)=
$((150/100)*(50/100)*100)=$75.
Decrease = 25%
Answer option B)25.
Answer: (B) 25
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Elaine?
(A) 1,008
(B) 1,296
(C) 1,512
(D) 2*1008
(E) 2,268
Rationale: Place D and H first: 8 options for D, 7 options for H
We are left with 6 empty places. A, B and C must take first 3 places and F, G, Emust take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for F, G, and E
Total = 8*7*3!*3! = 2*1008
Answer: D.
Answer: (D) 2*1008
Question: A room contains 180 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 25
(B) 35
(C) 45
(D) 55
(E) 65
Rationale: Say group of x people left the room.
# of women in the room was 0.15*180=27;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(180-x);
So, 27-0.3x= 0.1(180-x) --> x=45.
Answer: C.
Answer: (C) 45
Question: A can finish a piece of work in 4 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 2/4 + (2 + x)/10 = 1 => x = 3 days
Answer: A
Answer: (A) 3
Question: If a, b, c, and d are integers; w, x, y, and z are prime numbers; w < x < y < z; and (wa)(xb)(yc)(zd)=660(wa)(xb)(yc)(zd)=660, what is the value of (a + b) – (c + d)?
(A) –1
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: 660660= 2^2 x 3^1 x 5^1 x 11^1
w < x < y < z = 2 < 3 < 5 < 11
So, can can say -
w = 2
x = 3
y = 5
z = 11
Hence a = 2 , b = c = d = 1
(a + b) – (c + d) will be (2 + 1) – (1 + 1) = 1
Answer will be (C)
Answer: (C) 1
Question: 5358 x 51 = ?
(A) 273435
(B) 272651
(C) 273258
(D) 273898
(E) 273299
Rationale: C
5358 x 51 = 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
Answer: (C) 273258
Question: HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 10%
(A) 36
(B) 40
(C) 32
(D) 42
(E) 45
Rationale: Let the weight of tea(25 per kg) to be used - X
The total cost of the blend - total cost of 25 RS tea + total cost of 30 RS tea
- 25X + 900 ( as the total weight of 30 RS tea is already given i.e 30)
total weight of the blend = X + 30 ( which should be sold per 30 RS and result in 10% profit)
The equation follows like this
25X + 900 + (10 % of (25X + 900)) = 30( X + 30)
25X + 900 +2.5 X + 90 = 30 X + 900
27.5 X + 990 = 30 X + 900
2.5 X = 90
X= 90/2.5 = 36
ANSWER:A
Answer: (A) 36
Question: Round off the given number to nearest hundreds
10158
(A) 10000
(B) 10200
(C) 11000
(D) 10150
(E) 10100
Rationale: the given number is 10158
its tens digit is 5. so replace each of the tens and ones digit by 0 and increase the hundreds digit by 1 to get the rounded off number to the nearest hundred.
correct answer (B)
Answer: (B) 10200
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is:
(A) 2 : 3
(B) 5 : 3
(C) 6 : 7
(D) 9 : 16
(E) None of these
Rationale: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = âˆšb : âˆša = âˆš25 : âˆš9 = 5 : 3.
Answer B
Answer: (B) 5 : 3
Question: Each of 7 workers will pick a day of the week as his vacation day. What is the probability that exactly one worker will pick a different day?
(A) 7!/7^7
(B) 1/7!
(C) 1/7^7
(D) 7/7!
(E) 7/7^7
Rationale: Each worker out of 7 has 7 options (Sunday, Monday, Tuesday,.., Saturday), hence total # of outcomes is 7^7;
Favorable outcomes will be 7!, which is # of ways to assign 7 different day to 7 workers.
P=favorable/total=7!/7^7
Answer: A.
Answer: (A) 7!/7^7
Question: The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?
(A) 24
(B) 48
(C) 56
(D) 60
(E) 62
Rationale: H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.
ANSWER:D
Answer: (D) 60
Question: -84 x 29 + 365 = ?
(A) 2071
(B) 2436
(C) 2801
(D) -2801
(E) -2071
Rationale: E
Given Exp. = -84 x (30 - 1) + 365
= -(84 x 30) + 84 + 365
= -2520 + 449
= -2071
Answer: (E) -2071
Question: Set Q consists of the following five numbers: Q = {7, 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}
(A)  I only
(B)  III
(C)  IIII
(D)  IIIII
(E)  I, II,III
Rationale: (1)	Multiplying all the numbers change Standard Deviation
(2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number there in the Set Q.
Set II: elements are multiplied by 2 and standard deviation changes.
Hence the answer is A.
Answer: (A)  I only
Question: A dealer owns a group of station wagons and motorcycles. If the number of tires (excluding spare tires) on the vehicles is 30 more than twice the number of vehicles, then the number of station wagons the dealer owns is
(A) 10
(B) 15
(C) 20
(D) 30
(E) 45
Rationale: Assume X station wagons, Y motorcycles
Framing the equation.
2(X+Y)+30 = 4X + 2Y
=> X = 15
ANSWER:B
Answer: (B) 15
Question: What is the different between the place value and face value of 3 in the numeral 1375?
(A) 280
(B) 289
(C) 297
(D) 300
(E) 310
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
C)
Answer: (C) 297
Question: If 4a = 5b = 30, then 40ab =
(A) 900
(B) 1800
(C) 2250
(D) 1650
(E) 1250
Rationale: 4a * 5b = 30 * 30 = 900
20 ab = 900
i.e. 30 ab = 1800
Answer: Option B
Answer: (B) 1800
Question: In a room filled with 5 people, 3 people have exactly 2 siblings in the room and 2 people don't have any siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
(A) 3/5
(B) 4/5
(C) 3/10
(D) 7/10
(E) 9/10
Rationale: The 5 people consist of one set of 3 siblings and 2 other people who are not siblings.
The number of ways to choose 2 people is 5C2 = 10.
The number of ways to choose 2 from the group of siblings is 3C2 = 3.
The number of ways to choose 2 people who are not siblings is 10-3=7.
P(the two people are not siblings) = 7/10
The answer is D.
Answer: (D) 7/10
Question: A and B started a business with initial investments in the ratio 12 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?
(A) 42 months
(B) 8 months
(C) 9 months
(D) 5 months
(E) 7 months
Rationale: Let Sumit in the business for ‘a’ months.
Investment Ratio Amit to Sumith = 12:3
Profit sharing ratio = 8 : 7.
Amit is in the business for 12 months.
Then Sumit in the business for
(12 × 12) / (3 × a) = 8 / 7 => 24a = 1008 or
a = 1008 / 24 = 42 or 42 months
Option A
Answer: (A) 42 months
Question: What is the perimeter of a square field whose diagonal is 8√2?
(A) 33
(B) 32
(C) 88
(D) 99
(E) 221
Rationale: 4a = 32 m
Answer: B
Answer: (B) 32
Question: What are the last two digits of 5in2007th ?
(A) 75
(B) 65
(C) 55
(D) 25
(E) 05
Rationale: Just keep track of the last two digits of the consecutive powers of 5 and note
that 5-2round- = 25 and 5 × 25 = 125.
correct answer D
Answer: (D) 25
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 16
(B) 13
(C) 18
(D) 11
(E) 19
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer: C
Answer: (C) 18
Question: In Orange County one sixth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 60.
(B) 42.
(C) 85.
(D) 140.
(E) 252.
Rationale: The number must be an integer and multiple of both 6 and 7.
Only option B fulfill this condition and hence is the answer.
Answer: (B) 42.
Question: Pipe A can empty a tank in 12 hrs and pipe B can empty it in 24 hrs. If both the pipes are opened to empty in the fully filled tank . In how many hours will it be emptied tank?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Part emptied A in 1 hr= (1/12)
Part emptied B in 1 hr= (1/24)
Part emptied by (A+B) together in 1 hr=(1/12)+(1/24)=1/8
So, The tank will be empty in 8 hrs
Answer : C
Answer: (C) 8
Question: Sum of two numbers is 25 and their difference is 13. Find their product.
(A) 104
(B) 108
(C) 114
(D) 124
(E) 142
Rationale: Explanation:
Friends, this sort of question is quite important in competitive exams, whenever any question come which have relation between sum, product and difference, this formula do the magic:
=>(x+y)2=(x−y)2+4xy
<=>(25)2=(13)2+4xy
<=>4xy=(25)2−(13)2
<=>xy=456/4=114
Option C
Answer: (C) 114
Question: Of the families in City X in 1998, 20 percent owned a personal computer. The number of families in City X owning a computer in 2002 was 40 percent greater than it was in 1998, and the total number of families in City X was 8 percent greater in 2002 than it was in 1998. what percent of the families in City X owned a personal computer in 2002?
(A) 49.66%
(B) 52.66%
(C) 28.22%
(D) 33.33%
(E) 25.92%
Rationale: Say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 20
Number of families owning computer in 2002 = 20 * 140/100 = 28
Number of families in 2002 = 108
The percentage = 28/108 * 100 = 25.92%.
ANSWER:E
Answer: (E) 25.92%
Question: What is the remainder when 617 + 1176 is divided by 7?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 617 + 1176 mod 7
=> 617%7 + 1176%7
=> 1 + 0
=> 1%7
=> 1
ANSWER:A
Answer: (A) 1
Question: What percent of 60 is 100?
(A) 133 1⁄3
(B) 75
(C) 166.66
(D) 33 1⁄3
(E) 25
Rationale: % of 60 is 100?
= 100/60 = 5/3 = 166.66%
Thus C is the correct answer.
Answer: (C) 166.66
Question: If the average of ten numbers is 50, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 50
(A) I
(B) II
(C) III
(D) all three options
(E) I&II
Rationale: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.
IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.
D
Answer: (D) all three options
Question: The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is?
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: 2x 3x
8x cube + 27x cube = 945
35x cube = 945
x cube = 27 => x = 3
Answer:A
Answer: (A) 3
Question: If a and b are positive integers, and a=20b-15, the greatest common divisor of a and b CANNOT be
(A) 1
(B) 3
(C) 18
(D) 15
(E) 5
Rationale: If b is 1, 3, 5, or 15, then GCD of a and b is 1, 3, 5, and 15 respectively. So, by POE the answer must be C.
Still: if b is a multiple of 18, then a is 15 smaller than a multiple of 18, so not a multiple of 18, so both of them cannot be divisive by 18.
Answer: C.
Answer: (C) 18
Question: If an article with marked price of $600 is sold at successive discount of 10%,25% and 15%,what is the price the customer has to pay?
(A) 360
(B) 300
(C) 230
(D) 342
(E) 320
Rationale: discount=0.9*.75*.85=.57
so .57*600=342
ANSWER:D
Answer: (D) 342
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 4 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
(A) 16:00.
(B) 18:00
(C) 20:00
(D) 22:00.
(E) 24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 4 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 6 hours
Time taken by both buses to meet again in St. Louis will be LCM of 4 and 6 = 12
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 24:00 hours
Answer E
Answer: (E) 24:00.
Question: If x > 0, x/25 + x/20 is what percent of x?
(A) 5%
(B) 25%
(C) 37 1/2%
(D) 60%
(E) 75 %
Rationale: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/25 + 100/20= 4+5 =9
9 is 9% of 100=A.
Answer: (A) 5%
Question: If a is an integer greater than 2 but less than 7 and b is an integer greater than 4 but less than 13, what is the range of a/b?
(A) 23/34
(B) 57/60
(C) 51/67
(D) 19/71
(E) 75/64
Rationale: The way to approach this problem is 2<a<7 and 4<b<13
Minimum possible value of a is 3 and maximum is 6
Minimum possible value of b is 5 and maximum is 12
Range = max a/min b - min a/max b
(Highest - lowest)
6/5 - 3/12 = 57/60
Hence B
Answer: (B) 57/60
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?
(A) 150
(B) 377
(C) 297
(D) 266
(E) 971
Rationale: 5x + 12x + 13x = 300 => x = 10
a = 50, b = 120, c = 130
S = (50 + 120 + 130)/2 = 150
Answer: A
Answer: (A) 150
Question: A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the T % profit made by the merchant?
(A) 66.67 %
(B) 50 %
(C) 200 %
(D) 100 %
(E) 33.33 %
Rationale: C.P of 1 article= $30(say)
C.P of 20 articles=30*20=$600
Now, C.P of 20 articles=Profit on 30 articles
Therefore, profit on 1 article=$600/30=$20
Profit T%=(20/30)*100=66.67%
Answer A
Answer: (A) 66.67 %
Question: Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?
(A) 60 km/hr
(B) 70 km/hr
(C) 120 km/hr
(D) Data inadequate
(E) None of these
Rationale: Let their speed be x km/hr and y km/he respectively.
Then, 120/(x + y) = 1 => x + y = 120 --- (i)
Now, when they move in same direction:
(Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km
6x - 6y = 120 => x - y = 20 --- (ii)
Sloving (i) and (ii), we get x = 70, y = 50
P's speed = 70 km/hr.
ANSWER:B
Answer: (B) 70 km/hr
Question: Two heavily loaded sixteen-wheeler transport trucks are 940 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
(A) 90
(B) 130
(C) 150
(D) 140
(E) 450
Rationale: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:
Short version:
Truck A travels for an hour.
Distance remaining = 940-90 = 850k
Ratio of speeds 9:8 -> 850/17 = 50
Truck A = 90 + 50*9 = 540
Truck B = 50*8 = 400
Delta = 140km
Answer D
Answer: (D) 140
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 20 km/hr and second half at the rate of 20 km/hr. Find the total journey in km.
(A) 220 km
(B) 224 km
(C) 230 km
(D) 232 km
(E) 200 km
Rationale: 0.5x/20 + 0.5x/20 = 10
--> x/20 + x/20 = 20
--> 2x = 20 x 20
--> x = (20x20)/2 = 200 km.
Answer : E.
Answer: (E) 200 km
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 21 gallons of gasoline?
(A) 190
(B) 284.6
(C) 300
(D) 256
(E) 312
Rationale: so 12.2 * 21 = 256..
IMO option D is correct answer..
Answer: (D) 256
Question: What is the difference between the place value and face value of 4 in the numeral 46?
(A) 36
(B) 45
(C) 52
(D) 44
(E) 39
Rationale: Difference between the place value and face value of 4 = 40- 4 = 36
Answer is A
Answer: (A) 36
Question: Which of the following are roots of an equation (x^-2)+(x^-1)-20=0
(A) 1/5 and -1/4
(B) -1/5 and 1/4
(C) 1/5 and 1/4
(D) -1/5 and -1/4
(E) -5/2 and -1/4
Rationale: Given: (x^-2) + (x^-1) - 20 = 0
Rewrite as: 1/(x²) + 1/x - 20 = 0
Remove fractions by multiplying both sides by x² to get: 1 + x - 20x² = 0
Rearrange to get: 20x² - x - 1 = 0
Factor to get: (5x + 1)(4x - 1) = 0
So, EITHER 5x + 1 OR 4x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 4x - 1 = 0, then x = 1/4
So, the roots (solutions) are -1/5 and 1/4
The answer is B.
Answer: (B) -1/5 and 1/4
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in?
(A) 17 hours
(B) 12 hours
(C) 18 hours
(D) 10 hours
(E) 97 hours
Rationale: The part of the tank filled by three pipes in one hour
= 1/8
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
Answer:B
Answer: (B) 12 hours