mathewhe/aqua_rat huggingface dataset:
Question: Mangoes sell for $3.25 for a piece that costs a total of $2.85 to source. Oranges sell $2.80 for a piece that costs $2.65 to get. If you sell 55,000 mangoes in a month, how many oranges you must sell to make at least as much in total gross profit as for mangoes ?
(A) 7,858
(B) 8,301
(C) 14,667
(D) 63,840
(E) 146,667
Rationale: Mangoes : Profit/piece = 3.25-2.85 = 0.4
: No of pieces = 55,000
: Gross Profit = 55,000*0.4 = 22,000
Oranges : Profit/piece = 0.15
: Gross Profit = 22,000
: No of pieces = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)
Answer E
Answer: (E) 146,667
Question: A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
(A) 2.75
(B) 5.95
(C) 7.95
(D) 3.25
(E) 4.95
Rationale: Speed downstream =22/4 = 5.5 kmph
Speed upstream =22/5 = 4.4 kmph
Speed of the boat in still water=(5.5+4.4)/2= 4.95 kmph
Answer: E
Answer: (E) 4.95
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 640 is required to paint the floor at the rate of Rs. 5 per sq m, then what would be the length of the floor?
(A) 19.6m.
(B) 20.0m.
(C) 19.3m.
(D) 18.5m.
(E) 18.9m.
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 3b = 3b
Area of the floor = 640/5 = 128 sq m
l b = 128 i.e., l * l/3 = 128
l2 = 384 => l = 19.6m.
ANSWER:A
Answer: (A) 19.6m.
Question: If y exceeds x by 15%, then x is less than y by?
(A) 1/12%
(B) 1/17%
(C) 1/21%
(D) 1/22%
(E) 1/23%
Rationale: X=100	y=115
115------15
100-------? => 13 1/23%
Answer:E
Answer: (E) 1/23%
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $8. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 72/(xy)
(B) 90xy
(C) xy/90
(D) xy/10
(E) 10/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 8 / (xy/9) = 72/(xy).
The answer is A.
Answer: (A) 72/(xy)
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 26 years now, the son's age 3 years back was:
(A) 14 years
(B) 19 years
(C) 33 years
(D) 38 years
(E) 10 years
Rationale: Let the son's present age be x years. Then, (26 - x) = x
2x = 26
x = 13
Son's age 5 years back (13 - 3) = 10 years.
Answer: E
Answer: (E) 10 years
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 6 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 520
(B) 620
(C) 820
(D) 740
(E) 864
Rationale: Distance = (240 x 6) = 1440 km.
Speed = Distance/Time
Speed = 1440 /(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = (1440x3/5) km/hr = 864 km/hr
Answer E) 864 Km/hr
Answer: (E) 864
Question: In a sample of National college students, 30 percent are third year students and 60 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?
(A)  3/4
(B)  2/3
(C)  4/7
(D)  1/2
(E)  3/7
Rationale: = 40/70. = 4/7
my answer is C too
Answer: (C)  4/7
Question: In a class of 250 students, 130 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?
(A) 60%
(B) 40%
(C) 30%
(D) 20%
(E) 10%
Rationale: No of students study french= 250- No of students study spanish = 250-130=120
% of the students study french but not spanish = (120/200)*100 % = 60 %
Answer: A
Answer: (A) 60%
Question: Volume of a right circular cylinder is 6o L. If radius of cylinder is doubled, then what will be the increase in volume?
(A) 120 L
(B) 180 L
(C) 240 L
(D) 300 L
(E) 360 L
Rationale: Pi∗r^2∗h=60
double the radius.....Pi∗(2r)^2∗h=Pi∗4∗r^2∗h=4∗60=240
IMPORTANT.. we are looking at the increase so 240-60 = 180
ANSWER:B
Answer: (B) 180 L
Question: A 1000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 48
Rationale: In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (500 by that net inflow to get the minutes) - 6 min. Answer A.
Answer: (A) 6
Question: 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?
(A) A or V
(B) A or C
(C) A or B
(D) A or D
(E) A or J
Rationale: There are only 2 cases. Either left one is guilty or one of the remaining 9 to his right is guilty.
So If the left most is guilty, All the statements including the guilty one are lies. A and C are correct.
Or If Any one except left most one is guilty, Then one of the statements given by the person should be true. In this case all the suspects are lying does not hold. So If B is correct, A is not correct. i.e., only A or B is correct. Option C is correct.
Answer:C
Answer: (C) A or B
Question: The diagonals of a rhombus are 13 cm and 20 cm. Find its area?
(A) 176
(B) 130
(C) 150
(D) 179
(E) 172
Rationale: 1/2 * 13 * 20
= 130
Answer:B
Answer: (B) 130
Question: 30^10 / 240^5=?
(A) 6^5
(B) (15/4)^5
(C) 3^6
(D) 6^3
(E) 15^3
Rationale: 30^10 / 240^5=?
A. 6^5
B. (15/4)^5
C. 3^6
D. 6^3
E. 15^3
-> 30^10 / 240^5=(30^10)/(8^5)(30^5)=(30^5)/(8^5)=(2^5)(15^5)/(2^5)(4^5)=(15/4)^5.
Thus, B is the answer.
Answer: (B) (15/4)^5
Question: The school's basketball team scores for a five game series were 70, 75, 100, 70 and x. If their median score was 5 points lower than their average (arithmetic mean) score in the series, which of the following could be x?
(A) 75
(B) 80
(C) 85
(D) 90
(E) 95
Rationale: Look at the options available
Value of x seems to 75 < = x < = 95
A. 75
B. 80
C. 85
D. 90
E. 95
So position of x is fourth
70 , 70 , 75 , x , 100
Median = 75
Median score was 5 points lower than the average, so average = 80
70 + 70 + 75 + x + 100 = 400
x = 85 = Answer = C
Answer: (C) 85
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120
(B) 77
(C) 66
(D) 211
(E) 12
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
Answer: A
Answer: (A) 120
Question: Y is an even number and X is a positive odd number. Which of the following expressions cannot be even?
(A) X^3
(B) X*3Y*3
(C) (XY)^Y
(D) XY
(E) Y^2
Rationale: X^3 WILL BE ODD
A
Answer: (A) X^3
Question: A shop sells bicycles and tricycles. In total there are 8 cycles (cycles include both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
(A) b=2,t=3
(B) b=5,t=3
(C) b=6,t=2
(D) b=2,t=5
(E) b=3,t=4
Rationale: Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=8............(1)
2b+3t=19............(2)
Rearrange equation (1) and substitute into equation (2)
2b+24-3b=19
-b=-5
b=5
Calculate the number of tricycles t
t=8−b
=8−5
=3
There are 3 tricycles and 5 bicycles.
Answer is B.
Answer: (B) b=5,t=3
Question: How many seconds will a 150 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 12 sec
(B) 30 sec
(C) 86 sec
(D) 15 sec
(E) 18 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 150 * 3/50
= 15 sec.
Answer: D
Answer: (D) 15 sec
Question: What is the greatest of 3 consecutive integers whose sum is 24 ?
(A) 3
(B) 76
(C) 8
(D) 9
(E) 10
Rationale: Explanation:
The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 24;
=> 3n = 21;
=> n = 7
The greatest of the three numbers is therefore 7 + 2 = 9
Answer: D) 9
Answer: (D) 9
Question: Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 3. Based on this information, how many gold coins would there be in this collection after the proposed trade?
(A) 50
(B) 60
(C) 180
(D) 200
(E) 300
Rationale: The correct answer is C.
Answer: (C) 180
Question: An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
(A) 18,000 degrees / second
(B) 26,000 degrees / second
(C) 32,000 degrees / second
(D) 47,000 degrees / second
(E) 55,000 degrees / second
Rationale: 3000 revolutions / minute
= 3000*360 degrees / 60 seconds
= 18,000 degrees / second
correct answer A
Answer: (A) 18,000 degrees / second
Question: The ratio of flour to water to sugar in a recipe is 11:5:2. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 7.5 cups of water, how much sugar is required?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: The ratio of flour to water is 22:5.
The ratio of flour to sugar is 5.5:2=22:8.
The new ratio of flour to water to sugar is 22:5:8
If we need 7.5 cups of water, then we need 12 cups of sugar.
The answer is E.
Answer: (E) 12
Question: If a certain number X is divided by 62, the reminder is 7. what is the reminder when X+11 is divided by 31?
(A) 3
(B) 5
(C) 18
(D) 6
(E) 8
Rationale: X can be written as 62K + 7 or X = 7,69,131,etc.
X + 11 = 62K + 7+11= 62K +18 or X + 11 = 18,80,142 etc.
When divided by 31, we will get the remainder 18.
C
Answer: (C) 18
Question: The population of a city increases by 4% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
(A) 9%
(B) 9.27%
(C) 27%
(D) 12%
(E) None of these
Rationale: Actual increase in population=3%
Let, earlier population=100 then the population after 3 years
=100(1+3/100)^3=109.2727
∴Required percentage=9.27%
ANSWER:B
Answer: (B) 9.27%
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) 323
(B) 144
(C) 278
(D) 279
(E) 171
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144
Answer: B
Answer: (B) 144
Question: At the end of each year, the value of a certain antique watch is "c" percent more than its value one year earlier, where "c" has the same value each year. If the value of the watch was "k" dollars on January 1, 1992, and "m" dollars on January 1, 1994, then in terms of "m" and "k", what was the value of the watch, in dollars, on January 1, 1995?
(A) m+1/2(m-k)
(B) m+1/2((m-k)/k)m
(C) (m*sqrt(m))/sqrt(k)
(D) m^2/2k;
(E) km^2
Rationale: m = k*(1+c)^2
m/k = (1+c)^2
(m/k)^(1/2) = 1+c
c= (m/k)^(1/2) - 1
the value of the watch in jan 1 1995 is:
m(1+c)
so m(1+(m/k)^(1/2) - 1)
= m(m/k)^(1/2))
ANSWER:C
Answer: (C) (m*sqrt(m))/sqrt(k)
Question: A digital wristwatch was set accurately at 8.30 a.m and then lost 2 seconds every 5 minutes. What time was indicated on the watch at 6.30 p.m of the same day if the watch operated continuously that time ?
(A) 5.56
(B) 5.58
(C) 6.0
(D) 6.23
(E) 6.26
Rationale: for every 5 min watch looses 2 secs, so for 60 ms it looses 24 sec,
i.e., for 1 hr it looses 24 secs
8.30amto6.30pm=10 hr it looses 240 secs i.e., 4 mins , hence d watch will show 6.26
ANSWER:E
Answer: (E) 6.26
Question: Find out the C.I on Rs.8000 at 4% p.a. compound half-yearly for 1 1/2 years
(A) 489.66
(B) 406.07
(C) 406.04
(D) 306.03
(E) 306.01
Rationale: A = 8000(51/50)3
= 8489.66
8000
-----------
489.66
Answer:A
Answer: (A) 489.66
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes X of the competition are possible?
(A) 18
(B) 20
(C) 54
(D) 84
(E) 120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total X=84 outcomes
D
Answer: (D) 84
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,35) and (-5,15). Which can be the coordinate of fourth vertex?
(A) (-5,-5)
(B) (5,15)
(C) (-5,-35)
(D) (-5,10)
(E) (15,35)
Rationale: A(-5, 15)
B(5, 15)
C(5, 35)
X(-5, 35): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 35): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:E
Answer: (E) (15,35)
Question: X^Y + Y^X =2408
Find the values of X ?
(A) 2407
(B) 2408
(C) 2409
(D) 2405
(E) 32
Rationale: 2407^1+1^2407=2408
ANSWER:A
Answer: (A) 2407
Question: 30 pens and 75 pencils were purchased for 750. If the average price of a pencil was 2.00, find the average price of a pen.
(A) 20
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (750 – 150) = 600
∴ Average price of a pen = 600⁄60 = 20
Answer A
Answer: (A) 20
Question: The length and breadth of a square are increased by 40% and 30% respectively. The area of the rectangle so formed exceeds the area of the square by ?
(A) 82%
(B) 78%
(C) 80%
(D) 90%
(E) none of these
Rationale: Since Side1 x Side2 = Area
Therefore, net% change in area
= ( x + y + xy/100) %
= [40 + 30 + (40 x 30)/100]% or 82%.
Therefore, area is increased by 82%.
ANSWER:A
Answer: (A) 82%
Question: How many odd integers X between 200 and 600 are there such that their tens digit is even?
(A) 20
(B) 25
(C) 100
(D) 150
(E) 200
Rationale: The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;
Total X: 4*5*5=100.
Answer: C.
Answer: (C) 100
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 7 books and the last shelf contained 11 books, how many shelves does the bookcase have?
(A) 7
(B) 6
(C) 4
(D) 5
(E) 3
Rationale: Let x be the number of shelves.
No of books in the beginning =12*x
After taking out 21 books No of remaining books = 12x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 7*(x-1)+11
12x-21=7(x-1)+11
5x=25
x=5. Answer D
Answer: (D) 5
Question: The population of a town increased from 1,45,000 to 2,30,500 in a decade. The average percent increase of population per year is:
(A) 4.37%
(B) 5.8%
(C) 6.8%
(D) 8.75%
(E) None
Rationale: Explanation: Increase in 10 years = (230500 - 145000) = 85500.
Increase% = (85500/145000 x 100)% = 58%.
Required average = (58/10)% = 5.8%.
Answer: Option B
Answer: (B) 5.8%
Question: An article is bought for Rs.600 and sold for Rs.900, find the gain percent?
(A) 33 1/7%
(B) 33 1/6%
(C) 50%
(D) 38 1/3%
(E) 33 2/3%
Rationale: 600 ---- 300
100 ---- ? => 50%
Answer:C
Answer: (C) 50%
Question: If x ≠ 0 and x - (2+ x^2)/x = y/x, then y =
(A) -5
(B) -2
(C) -4
(D) -3
(E) -1
Rationale: x - (2+ x^2)/x = y/x
x^2 -2 - x^2/x = y/x
y= -2
Answer : B
Answer: (B) -2
Question: tell the smaller no. if its subtraction is 5 and ration is 4:3.
(A) 15
(B) 10
(C) 8
(D) 5
(E) 4
Rationale: 4x-3x=5
x=5
smaller no.=15
answer A
Answer: (A) 15
Question: Vinay got thrice as many marks in Maths as in English. The proportion of his marks in Maths and History is 4:3. If his total marks in Maths, English and History are 250, what are his marks in English ?
(A) 120
(B) 90
(C) 40
(D) 80
(E) 70
Rationale: Explanation:
M=3E and M/H=4/3
H=3/4M=3/4×3E=9/4E
Now, M+E+H=250⇒ 3E+E+9/4E=250
25E = 1000 or E = 40
Correct Option: C
Answer: (C) 40
Question: When positive integer N is divided by positive integer J, the remainder is 16. If N/J = 134.08, what is value of J?
(A) 22
(B) 56
(C) 78
(D) 112
(E) 200
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 16
So, 134.08 = 134 + 16/J
So, J = 200 ANS E
Answer: (E) 200
Question: The difference between the ages of A and B is 10 years. Ten years ago, A was twice as old as B. Find the age of A, 10 years hence.
(A) 20 years
(B) 30 years
(C) 40 years
(D) 50 years
(E) 60 years
Rationale: given that A-B=10 ->(1)
A-10=2(B-10)
A=2B-10 ->(2)
by solving 1&2
we get A=30,B=20
After 10 years age of A is 40 years
ANSWER:C
Answer: (C) 40 years
Question: What is the sum of natural numbers between 40 and 100
(A) 4800
(B) 4270
(C) 5000
(D) 5500
(E) 5550
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 40 and 100 numbers = 61 => 100 - 40 = 60 + 1 = 61
Sn = 61/2 Ã— 140 = 61 Ã— 70 = 4270
Answer : B
Answer: (B) 4270
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
(A) 8.5 m
(B) 17 m
(C) 34 m
(D) 51 m
(E) None of these
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
ANSWER:B
Answer: (B) 17 m
Question: If e is a positive integer, then 3^e + 3^(e +1) =
(A) 4^a
(B) 3^a − 1
(C) 3^(2a) + 1
(D) 3^a*(a − 1)
(E) 4(3^e)
Rationale: 3^e + 3^(e +1)
= 3^e + (3^e * 3^1)
= 3^e (1 + 3)
= 3^e(4)
Ans. E) 4(3^e)
Answer: (E) 4(3^e)
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 400 m?
(A) 122.9 m
(B) 127.5 m.
(C) 122.2 m
(D) 85 m
(E) 12289 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 400 m, the number of meters by which A beats C = (400 * 212.5)/1000
= 85m.
Answer:D
Answer: (D) 85 m
Question: Two representatives must be selected from each of two groups of students. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 1/2
Rationale: Group 1: 3 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*1*1*2 = 6 ways
Total Favorable cases = 3+6 = 9
Total Possible ways of selecting students 2 from each group = 4C2*3C2 = 6*3 = 18
Probability = 9/18 = 1/2
Answer : Option E
Answer: (E) 1/2
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITH', if repetition of letters is not allowed?
(A) 690
(B) 336
(C) 740
(D) 760
(E) 780
Rationale: The word 'LOGARITH' has 8 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 8P3
=
8
×
7
×
6
=
336
Option B
Answer: (B) 336
Question: Janet has to pay back her bank loan over 10 months following the below sequence.
$50, $55, $65, $80, $85, $95, $110, $115, $125, ?
How much will she pay back on the tenth month?
(A) $155
(B) $140
(C) $135
(D) $125
(E) $130
Rationale: The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140
Ans B
Answer: (B) $140
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:6
(C) 2:9
(D) 2:1
(E) 2:4
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Answer: (A) 2:5
Question: If taxi fares were $1.00 for the first 1/5 mile and $0.20 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was
(A) $1.56
(B) $2.40
(C) $3.80
(D) $4.20
(E) $2.80
Rationale: In 3 miles , initial 1/5 mile charge is $1
rest of the distance = 3 - (1/5) = 14/5
rest of the distance charge = 14(0.2) = $2.8 (as the charge is 0.2 for every 1/5 mile)
=> total charge for 3 miles = 1+2.8 = 3.8
Answer is C.
Answer: (C) $3.80
Question: The average of 20, 100 and 180 is twice the average of 10, 30, and which of the following ?
(A) 1)110
(B) 2)30
(C) 3)60
(D) 4)90
(E) 5)180
Rationale: 20 100 180 = 180+120 = 300/3 = 100
100/2 = 50
10 30 x = 40+x/3 should be smaller than 50
cross multiply 50*3-40 = 110
A
Answer: (A) 1)110
Question: A person was dialing a telephone. He forgot the last three digits of the six-digit telephone number but rembered that the number formed by the last three digits in the same order was a perfect square. What is the probability he dialed a right number?
(A) 1/32
(B) 1/46
(C) 1/49
(D) 1/36
(E) 1/18
Rationale: There are following perfect squares less than 1,000:
000 (0^2);
001 (1^1);
004;
009;
016;
025;
036;
049;
064;
081;
100;
121;
144;
...
961 (31^2).
Total of 32 perfect squares.
The probability = 1/32.
Answer: A.
Answer: (A) 1/32
Question: A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ?
(A) 249
(B) 498
(C) 676
(D) 823
(E) 274
Rationale: slope of 2 and a y-intercept of 2
y-coordinate is 550
y = 2x + 2
548 = 2x
x = 274
Answer:
E. 274
Answer: (E) 274
Question: A grandmother lent $20,000 to her grandson at the beginning of the year. At the end of the year, she received y dollars more than than the amount she lent due to interest. She also received an additional amount $300, as a gift. In terms of y, what fraction of the amount that grandmother received was the gift?
(A) 50Y
(B) 300/(20300+Y)
(C) 300Y/20000Y
(D) 2/3Y
(E) 300Y/(Y+1)
Rationale: The amount of money the grandmother received was (20,000 + 300+ y) dollars. The $300 gift as a fraction of the amount received was, therefore, 300/(20,300 + y).
Answer: B.
Answer: (B) 300/(20300+Y)
Question: The diagonal of a rectangle is sqrt(41) cm. and its area is 20 sq. cm. The perimeter of the rectangle must be:
(A) 22
(B) 18
(C) 19
(D) 27
(E) 62
Rationale: Explanation:
\inline {\color{Black}\sqrt{l^{2}+b^{2}}=\sqrt{41}}
Also, lb=20
\inline {\color{Black}(l+b)^2=(l^{2}+b^{2})+2lb=41+40=81}
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
Answer: B) 18 cm
Answer: (B) 18
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 0
II. x = 0
III. x =y
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer B
Answer: (B) II only
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
(A) 600
(B) 729
(C) 278
(D) 268
(E) 308
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
Answer: (A) 600