divelab/Sys2Bench huggingface dataset:
Question: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
Options:
A)6 %
B)6.1 %
C)6.2 %
D)6.3 %
E)6.4
Rationale: Solution:
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer : E
Answer: E
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 10 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Options:
A) 250
B) 625
C) 1,250
D) 2,500
E) 10,000
Rationale: total fish = x
percentage of second catch = (10/50)*100 = 20%
so, x * 20% = 50
x = 250 ans A.
Answer: A
Question: Find the greatest number of five digits which is exactly divisible by 12, 15 and 18?
Options:
A)A)13050
B)B)12960
C)C)10025
D)D)11080
E)E)12080
Rationale: The largest five digit numbers are
13050,12960,12080
13050 is not divisible by 12
12960 is divisible by 18, 12 and 15
ANSWER:B
Answer: B
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Options:
A)60 m
B)20m
C)43m
D)20m
E)23m
Rationale: To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers 4	x 360	m	= 480 m.
3
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m.
Answer:	D
Answer: D
Question: Average of first six multiples of 4 is
Options:
A)9
B)11
C)14
D)15
E)17
Rationale: Explanation:
Average=4(1+2+3+4+5+6) / 6=64 / 6=14
Option C
Answer: C
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
Options:
A)Rs.4500
B)Rs.5200
C)Rs.1800
D)Rs.3000
E)Rs.3200
Rationale: Explanation:
A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
ANSWER IS D
Answer: D
Question: The average of first 80 non-zero positive numbers is:
Options:
A)22.25
B)31.25
C)35
D)40.5
E)None of these
Rationale: Explanation :
Sum of first n natural numbers = n (n + 1)/2
So, average of first n natural numbers =
n (n + 1)/2n = (n + 1)/2
Required average = (80 + 1)/2 = 81/2 = 40.5.
Answer : D
Answer: D
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
Options:
A)152600m2
B)153500m2
C)153600m2
D)153800m2
E)None of these
Rationale: Explanation:
Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.
We are having speed and time so we can calculate the distance or perimeter in this question.
Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Lets solve it:
Perimeter = Distance travelled in 8 minutes,
=> Perimeter = 12000/60 * 8 = 1600 meter. [because Distance = Speed * Time]
As per question length is 3x and width is 2x
We know perimeter of rectangle is 2(L+B)
So, 2(3x+2x) = 1600
=> x = 160
So Length = 160*3 = 480 meter
and Width = 160*2 = 320 meter
Finally, Area = length * breadth
= 480 * 320 = 153600 Answer: Option C
Answer: C
Question: Four bells begin to ring together and they ring after an interval of 6,8,9 and 12 second respectively. How many times will they ring together in one hour, including the one at the start?
Options:
A)50
B)56
C)62
D)51
E)55
Rationale: LCM is 72. So they ring together in every 72 sec.
there are 3600 sec in 1 hr. so, 3600/72=50.
and 1 ring at the beginning. makes it 51.
ANSWER:D
Answer: D
Question: Find a number such that when 15 is subtracted from 7 times the number, the
Result is 10 more than twice the number.
Options:
A)1
B)4
C)5
D)0
E)3
Rationale: Let the number be x. Then, 7x - 15 = 2x + 10 => 5x = 25 =>x = 5.
Hence, the required number is 5.
Answer is C.
Answer: C
Question: Solve below question 3x - 5 = -20
Options:
A)-8
B)-9
C)-5
D)-4
E)1
Rationale: 1. Subtract 1 from both sides: 3x - 5 + 5 = -20 + 5 2. Simplify both sides: 3x = -15 3. Divide both sides by 3: 4. Simplify both sides: x = -5 C
Answer: C
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)78
B)72
C)90
D)27
E)23
Rationale: SP of m of cloth
= 8925/85 = Rs. 105
CP of 1m of cloth
= SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15
= Rs. 90.
Answer: C
Answer: C
Question: Lorna invests $4000, 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)$800
D)$4,400
E)$5,840
Rationale: We have that 'x' invested at 6%
We also have that 4000-x' invested at 11%
Now then 580/4000 is approx 10%
Therefore, -4x+4000-x=0
5x=4000
x=800 approximately. Probably higher
Only C matches
Answer: C
Question: There are 2 more women than there are men on a local co-ed softball team. If there are a total of 16 players on the team, what is the ratio of men to women?
Options:
A)10/16
B)6/16
C)4/16
D)7/9
E)4/10
Rationale: w = m+2
w+m = 16
m+2+m = 16
2m = 14
m = 7
w = 9
ratio:7:9
Ans: D
Answer: D
Question: What percent of 200 is 55?
Options:
A)0.25%
B)4%
C)25%
D)27.5%
E)250%
Rationale: 200*x /100 = 55
x = 27.5
Ans: D
Answer: D
Question: A number a is squared and then multiplied by negative 4. The result of this operation is equal to 4times the sum of FOURTH times a and 1. What is one possible value of a ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: -4*a^2=4(4a+1)
a= -1 or -1
a=-1=B
ANSWER:A
Answer: A
Question: 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 4 women and 10 children together complete the piece of work?
Options:
A)5 days
B)15 days
C)28 days
D)6 days
E)7 days
Rationale: Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
4 women’s 1 day’s work = 1/192 × 4 = 1/48
1 child’s 1 day’s work = 1/240
10 children’s 1 day’s work = 1/24
Therefore, (10 men + 4 women + 10 children)’s 1 day’s work = 5/48 + 1/48 + 1/24
= 8/48 =1/6
The required No. of days = 6 days
Answer: Option D
Answer: D
Question: The rate fo simple interest in two banks is in the ratio of 4 : 5 . Amith wants to deposit his total saving in these two banks in such a way that he should receive equal half yearly interest from both. He should deposits the saving in the banks in the ratio of:
Options:
A)2 : 5
B)5 : 4
C)5 : 3
D)4 : 5
E)1 : 2
Rationale: Let the savings be X and Y and the rates of simple interest be 4x and 5x respectively.
Then X +4x * 1/2 *1/100 = Y + 5x * 1/2 *1/100
or X/Y = 5/4
i.e. X : Y = 5 : 4
ANSWER:B
Answer: B
Question: The retail price of a washing machine is Rs.1265. If the manufacturer gains 10%, the wholesale dealer gains 15% and the retailer gains 25%, then the cost of the product is
Options:
A)Rs 800
B)Rs 900
C)Rs 700
D)Rs 600
E)Rs 500
Rationale: Suppose the cost = Rs X
Therefore, S.P. of the manufacturer = X + 10% of X = 11X/10
S.P. of the wholesale dealer = 11X/10 + 15% of 11X/10 = 11X/10 + 33X/200 = (253/200) X
S.P. of the retailer = 253/200 X + 25% of 253/200X = 253/200 X + 253/800 X = (1265/800) X
Given (1265/800) X = 1265 => X = Rs. 800
ANSWER:A
Answer: A
Question: Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case.
Options:
A)35
B)25
C)15
D)45
E)None of them
Rationale: Required number = H.C.F. of (132 - 62), (237 - 132) and (237 - 62)
= H.C.F. of 70, 105 and 175 = 35.
Answer is A.
Answer: A
Question: There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems
Options:
A)36
B)60
C)45
D)72
E)90
Rationale: Let x = minutes spent on a non-math problem
then 2x = minutes spent on a math problem
x(200-50) + 2x(50) = 180
x(150) + 2x(50) = 180
150x + 100x = 180
250x = 180
x = 0.72 minutes
Time to spend on math problems:
2x(50)=100x = 100(0.72) = 72 minutes ANSWER :D
Answer: D
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 less than n. What is y in terms of x ?
Options:
A) 20 - x
B) 9 - x
C) x + 9
D) x - 1
E) x + 1
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 9 less than 10x+y
10x+y-9=10y+x
10x-x-9=10y-y
9x-9=9y
x+1=y
OR
y=x-1
Ans:D
Answer: D
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
Options:
A)30
B)40
C)45
D)48
E)54
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
B)
Answer: B
Question: A train of 30 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
A)6
B)3.3
C)4
D)9
E)2
Rationale: D = 30 * 60 + 1500 = 3300 m
T = 3300/60 * 18/5 = 198 sec = 3.3 mins
Answer:B
Answer: B
Question: A person spent 1/5 of his salary last year on household and 1/4 of the remainder on clothes. What fraction of last year’s salary did the person have left after his household and clothes expenditures?
Options:
A)2/3
B)3/5
C)2/6
D)5/4
E)1/2
Rationale: The person spent 1/5 of his salary on household, so remaining is 4/5
1/4 of the remaining is spent is spent on clothes, 1/4*4/5 is 2/10
To make the denominator common, we use 10, so 1/5=2/10
Total amount spent=2/10+2/10=4/10 is the total amount spent on household and clothes
Remaining salary is 6/10 of the total salary reduced to 3/5
Answer is B
Answer: B
Question: I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, how many possible committees are there?
Options:
A)12
B)44
C)56
D)120
E)200
Rationale: 6C3*4C2
=120=D
Answer: D
Question: Find 20 % of 240
Options:
A)96
B)94
C)86
D)74
E)48
Rationale: We know that R % of m is equal to R/100 × m.
So, we have 20 % of 240
20/100 × 240
= 48
Answer:E
Answer: E
Question: In what ratio must rice at Rs 9.30 per Kg be mixed with rice at Rs 10.80 per Kg so that the mixture be worth Rs 10 per Kg?
Options:
A)5:7
B)8:7
C)7:3
D)3:8
E)4:7
Rationale: Cost of 1 kg of 1st kind=930 P
Cost of 1 kg of 2nd kind=1080 P
Mean Price=1000 P
Cost of 1 kg of 1st kind - Mean Price=1000-930= 70
Cost of 1 kg of 2nd kind- Mean Price=1080-1000=80
Required ratio = 80 : 70 = 8 : 7
Answer:B
Answer: B
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is
Options:
A)48
B)22
C)56
D)27
E)35
Rationale: Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
Answer: Option A
Answer: A
Question: A dealer sells his goods 10% less at cost price uses 850gm weight for 1kg his gain or loss percentage is
Options:
A)21% Gain
B)21% Loss
C)17 11/17% Gain
D)17 11/17% Loss
E)None of these
Rationale: Explanation:
Cost price ---> 850
Selling price --->1000 - 100 = 900
= ( 900 ~ 850 )/850 * 100 = 150/850 * 100 = 17 11/17% Gain
Answer: Option C
Answer: C
Question: Find the circumference of radius 7 cm.
Options:
A)44
B)55
C)66
D)77
E)88
Rationale: Circumference of circle = 2πr
= 2 × 22/7 × 7
= 44 cm
ANSWER : A
Answer: A
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is
Options:
A)12 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)None of these
Rationale: Explanation:
Rate upstream = (7/42)*60 kmh = 10 kmph.
Speed of stream = 3 kmph.
Let speed in sttil water is x km/hr
Then, speed upstream = (x —3) km/hr.
x-3 = 10 or x = 13 kmph
Option B
Answer: B
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $220?
Options:
A)1,108
B)2,100
C)2,108
D)2,124
E)2,218
Rationale: I can buy 9 250-pack for Rs 22.95*9 = $206.55
Now, I can buy 5 20-pack for 3.05*5 = $15.25
Now, I am left with only $1.15. I cannot but anything with this.
Hence Total Hotdogs = 250*8 + 20*5 = 2218
E
Answer: E
Question: Of the science books in a certain supply room, 50 are on botany, 60 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
Options:
A)81
B)159
C)309
D)285
E)324
Rationale: First, you can take all 50 Botany books, all 60 zoology books and all 40 geology books because you're sure to never pick 80 of them.
There are still 90 on physics and 110 on chemistry
The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.
Minimum number of books picked to reach 80 in the same science should be : 50 + 60 + 40 + 79 +79 + 1 = 309
C
Answer: C
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5.
Options:
A)18
B)20
C)24
D)30
E)32
Rationale: Solution
Average	= (10+15+20+25+30/5)
= 100 / 5
= 20.
Answer B
Answer: B
Question: How many 5 digit no. can b formed with digits 1, 2, 3,4,5,6 which r divisible by 4 and digits not repeated?
Options:
A)189
B)190
C)191
D)192
E)193
Rationale: for a no. to be divisible by 4, last two digit should be divisible by 4
last tw0 digit can be 12,16,24,32,36,52,56,64 (8 possibilities)
remaining 3 places can be filled in 4*3*2 ways for each
total 5 digit no. formed = 8*4*3*2 = 192
ANSWER:D
Answer: D
Question: In a school seats for Maths, Physics and Biology in a school are in the ratio 1:2:3. There is a proposal to increase these seats by 10%,20% and 30%. What will be the ratio of increased seats?
Options:
A)1:4:9
B)16:34:47
C)11:24:39
D)15:42:77
E)5:15:26
Rationale: Let the number of seats of M,P,B be x,2x,3x
Number of increased seats are 110% of x , 120% of 2x , 130% of 3x
x*110/100 , 2x*120/100 and 3x*130/100
i.e. 11x/10, 12x/5 and 39x/10
Required ratio = 11x:24x : 39x = 11:24:39
Answer is C
Answer: C
Question: In an election between the two candidates ,The candidates who gets 60% of votes polled is wined by 280 votes majority. What is the total number of votes polled?
Options:
A)1400
B)1500
C)1600
D)1700
E)1800
Rationale: Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %)
20 % = 60 % - 40 %
20% -----> 280 (20×14 = 280 )
100% -----> 1400 (100×14 = 1400)
A
Answer: A
Question: The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 m. The length of the hall is?
Options:
A)22
B)25
C)27
D)19
E)12
Rationale: Let breadth = x m
Then, length = (x+5)m
x(x+5) = 750
x² + 5x - 750= 0
(x+30)(x-25)= 0
x = 25
Answer: B
Answer: B
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)32:42
B)32:41
C)32:45
D)32:49
E)32:47
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer: C
Answer: C
Question: A sum of Rs.4500 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)Rs.2925
B)Rs.3120
C)Rs.3320
D)Rs.2760
E)None of these
Rationale: Let A be the amount received at the end of the three years.
A = 4500[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4500 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7425
So the interest = 7425 - 4500 = Rs.2925
ANSWER:A
Answer: A
Question: If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
Options:
A)3 days
B)4 days
C)5 days
D)6 days
E)7 days
Rationale: Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, (6x + 8y) = 1/10 and (26x + 48y) = 1/2.
Solving these two equations, we get : x = 1/100	and y = 1/200.
(15 men + 20 boy)'s 1 day's work = (15/100 + 20/200) = 1/4.
Therefore, 15 men and 20 boys can do the work in 4 days.
CORRECT OPTION: "B".
Answer: B
Question: A train running at the speed of 180 km/hr crosses a pole in 18 seconds. What is the length of the train?
Options:
A)800
B)900
C)950
D)1000
E)1050
Rationale: Speed=(180 x(5/18)m/sec	=(50)m/sec.
Length of the train = (Speed x Time).
Length of the train =	((50)x 18)m = 900 m
B
Answer: B
Question: If (4,000)(5,000) = (20)(1,000^x), what is the value of x?
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: (4,000)(5,000) = (20)(1,000^x)
=> (4,000)(5,000)/20 = 1,000^x
=> 1,000,000 = 1,000^x
=> 1,000^2 = 1,000^x
Since, base is same so powers will be same too.
So, x=2
Answer will be D
Answer: D
Question: If a certain number of labours can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of labours will require to dig earth 75m deep, 20m long and 50m broad.
Options:
A)12
B)18
C)6
D)1
E)2
Rationale: Explanation :
More number of days means more length, more depth and more width. Hence, its a direct proportion.
(100*25*30):(75*20*50) :: 12:x
75000:75000::12:x
x = 12
Answer : A
Answer: A
Question: In a bag there are a certain number of orange balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of orange balls to blue balls in the bag
Options:
A)2:1
B)1:1
C)1:31
D)1:3
E)1:5
Rationale: since the probability of drawing a blue ball out of two picks is 1/2.
the ratio of the blue ball to orange balls should be 1:1
Answer : B
Answer: B
Question: The simple interest on a sum of money will be Rs.400 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Options:
A)2261
B)2888
C)1200
D)800
E)2771
Rationale: P --- 10 ---- 400
P --- 5 ----- 200
3P --- 5 ----- 600
------
=> 800
Answer: D
Answer: D
Question: Club X has more than 20 but fewer than 50 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 4 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The number of members is 4j+3 = 5k+4.
Let's start at 4(5)+3 = 23 and keep adding 4 until we find a number in the form 5k+4.
23, 27, 31, 35, 39 = 5(7) + 4
The club has 39 members.
39/6 = 6(6) + 3
The answer is C.
Answer: C
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.144 in 4 Years?
Options:
A)5%
B)8%
C)3%
D)4.5%
E)1%
Rationale: 144 = (800*4*R)/100
R = 4.5%
Answer: D
Answer: D
Question: A man can row upstream at 40 kmph and downstream at 52 kmph, and then find the speed of the man in still water?
Options:
A)27
B)40
C)42
D)46
E)24
Rationale: US = 40
DS = 52
M = (40 + 52)/2
= 46
Answer:D
Answer: D
Question: Find the value of x from the below equation: x^2−7x+10=0
Options:
A)5 or 2
B)1 or 3
C)1 or 7
D)3 or 5
E)None
Rationale: Here we need to find out a and b such that a + b = -7 and ab = +10
a = -5 and b = -2 satisfies the above condition.
Hence
x^2−7x+10=(x−5)(x−2)
x2−7x+10=(x−5)(x−2)
x^2−7x+10
=0
⇒(x−5)(x−2)
=0
x2−7x+10=0⇒(x−5)(x−2)=0
Step 3: Equate each factor to 0 and solve the equations
(x−5)(x−2)
=0
⇒(x−5)
=0or (x−2)=0
⇒x= 5 or 2
A
Answer: A
Question: In a certain store, the profit is 150% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)30%
B)70%
C)100%
D)50%
E)120%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 150, S.P. = Rs. 250
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 250
Profit = 250 - 125 = Rs. 125
Required percentage = 125/250 * 100 = 50%
ANSWER:D
Answer: D
Question: What percent of a day is six hours?
Options:
A)20.83%
B)25%
C)18x2/3%
D)22x1/2%
E)None of these
Rationale: Explanation :
Required percentage = (6/24100)%
= 25%.
Answer : B
Answer: B
Question: Pipe A fills a tank in 6 minutes. Pipe B can fill the same tank 2 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
Options:
A)0.5
B)1.0
C)1.5
D)2.0
E)2.5
Rationale: A's rate is 1/6 and B's rate is 1/3.
The combined rate is 1/6 + 1/3 = 1/2
The pipes will fill the tank in 2 minutes.
The answer is D.
Answer: D
Question: For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?
Options:
A)22%
B)40%
C)60%
D)84%
E)94%
Rationale: Again, the exact dimensions of the cylinder do not matter, as long as every length increases by the same percent or same ratio. We now have a percent decrease, which means we subtract to construct our multiplier. A 60% decrease means we have a multiplier of 1 – 0.60 = 0.4, and so k = 0.4 as well. For volume we need to cube the scale factor: k^3 = (0.4)^3 = 0.064 {approx} 0.06 approximately. That would be the multiplier for a 94% decrease, because 1 – 0.94 = 0.06; therefore, the volume decreases by 94%. Answer = E.
Answer: E
Question: The C.P of 20 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: 20 CP = 12 SP
20 --- 8 CPgain
100 --- ? => 40%
Answer: D
Answer: D
Question: Divide $5000 among X,Y in the ratio 2:8. How many $ that X get?
Options:
A)$1000
B)$1050
C)$1100
D)$1150
E)$1200
Rationale: Sum of ratio terms = 2+8 = 10
X = 5000*2/10 = $1000
Answer is A
Answer: A
Question: There are 250 doctors and nurses at a hospital. If the ratio of doctors to nurses is 2 to 3, how many nurses are at the hospital?
Options:
A)134
B)138
C)142
D)146
E)150
Rationale: The number of nurses at the hospital is (3/5)*250=150.
The answer is E.
Answer: E