divelab/Sys2Bench huggingface dataset:
Question: Guadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters?
Options:
A)3,360
B)307,500
C)621,500
D)704,000
E)2,816,000
Rationale: One is 300 m by 500 m and the other is 250 m by 630 m :
(300*500)+(250*630) = 150000+157500
307500
ANSWER:B
Answer: B
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
Options:
A)3:5
B)3:3
C)3:9
D)3:1
E)3:2
Rationale: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2
=>3:1
Answer: D
Answer: D
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
Options:
A)3449
B)3777
C)2998
D)2420
E)2778
Rationale: Speed of the sound = 1100 ft/s
Time = 11/5 second
Distance = Speed × Time = 1100 ×115=220×11=2420 ft
Answer : D
Answer: D
Question: Which of the following is closest to 10^150 – 10^30 ?
Options:
A)10^210
B)10^180
C)10^150
D)10^90
E)10^6
Rationale: 10^150 – 10^30
10^30 * (10^120 – 1)
as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^120 – 1) would remain as 10^120.
and 10^30 * 10^120 = 10^150. Answer is C.
Answer: C
Question: If two numbers are in the ratio 6:7. If 10 is Reduced to both of the numbers then the ratio becomes 5:6 then find the smallest number?
Options:
A)50
B)30
C)60
D)70
E)80
Rationale: Explanation:
6:7
6x - 10 : 7x - 10 = 5 : 6
6[6x - 10] = 5[7x - 10]
36x - 60 = 35x - 50
36x - 35x = 60 - 50
x = 10
the small number is = 6
6x = 60 (Answer = 60)
Short cut method:
a:b = 6:7
c:d = 5:6
1.Cross multiplication with both ratios
a * d ~ b * c = 6 * 6 ~ 7 * 5 = 36 ~ 35 = 1
2. If 10 is reduced both the number means 10 * 5 = 50 and 10 * 6 = 60,
Then 50 ~ 60 = 10
===> 1 -----> 10
===> 6 -----> 60 (Answer is = 60)
Answer: Option C
Answer: C
Question: In some quantity of ghee, 60% of pure ghee and 40% of is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was?
Options:
A)5kg
B)10kg
C)15kg
D)20kg
E)25kg
Rationale: Let the original quantity be x kg
vanaspati ghee in x kg = 40/100 *x = 2x/5 kg
(2x/5)/(x+10) = 20/100
2x/(5x+50) = 1/5
5x = 50
x = 10kg
Answer is B
Answer: B
Question: There are 20 balls in a jar. You take out 2 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?
Options:
A)12.
B)9.
C)8.
D)7.
E)6.
Rationale: 12 = 3 blue balls + 18 / 2
Answer: A
Answer: A
Question: The present population of a town is 3600. Population increase rate is 20% p.a. Find the population of town before 2 years?
Options:
A)2500
B)2100
C)3500
D)3600
E)2050
Rationale: P = 3600
R = 20%
Required population of town = P/(1 + R/100)^T
= 3600/(1 + 20/100)^2
= 3600/(6/5)^2
= 2500(approximately)
Answer is A
Answer: A
Question: Anita, Indu and Geeta can do a piece of work in 18 days, 27 days and 36 days respectively. They start working together. After working for 4 days. Anita goes away and Indu leaves 7 days before the work is finished. Only Geeta remains at work from beginning to end. In how many days was the whole work done?
Options:
A)16 days
B)66 days
C)77 days
D)44 days
E)33 days
Rationale: :
4/18 + (x -7)/27 + x/36 = 1
x = 16 days
Answer: A
Answer: A
Question: The sides of a cube measures 6.5cm. If the surface area of the cube is the same as a ball, what is the radius of the ball? Round to the nearest whole number.
Options:
A)9
B)7
C)4
D)8
E)6
Rationale: First calculate the surface area of the cube. The cube is made of 6 squares with the sides measuring 6.5cm each. The surface area of 1 side of the cube is 42.25cm. Multiply the surface area of the 1 side by 6 will give you the cube's total surface area. The cubes surface area is 253.5cm. Now we know that the surface area of the ball is 253.5cm. To find out the surface area of a sphere you need to square the radius, then multiply by Pi, and multiply by the number 4. Going backwards to find the radius - you will need to dived the surface area by 4. Then divide by Pi. Then determine the square root of the answer. The radius is 4.460. Rounding to the nearest whole number the radius is 4. The correct answer is (C).
Answer: C
Question: If the side length of Square B is four times that of Square A, the area of Square B is how many times the area of Square A?
Options:
A)20
B)16
C)12
D)8
E)4
Rationale: Let x be the side length of Square A.
Then the area of Square A is x^2.
The area of Square B is (4x)^2=16x^2.
The answer is B.
Answer: B
Question: W, X and Y invested Rs.8100, Rs.7200 and Rs.2700 respectively, in a partnership business. Find the share of Y in profit of Rs.60000 after a year?
Options:
A)3000
B)6000
C)9000
D)12000
E)15000
Rationale: Explanation:
8100:7200:2700
9:8:3
3/20 * 60000 = 9000
C)
Answer: C
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 10
Options:
A)5/13
B)2/15
C)1 by 12
D)3/17
E)6/19
Rationale: Total number of cases = 6*6 = 36
Favourable cases = [(5,6)(6,5),(6,6)] = 3
So Probability = 3/36 = 1/12
Answer is C
Answer: C
Question: What is the sum of the first 24 natural numbers (starting from 1)?
Options:
A)250
B)300
C)350
D)400
E)450
Rationale: The sum of n natural numbers = n*(n+1) / 2 = 24*25/2 = 300
The answer is B.
Answer: B
Question: Evaluate: 20 - 12÷4×2 =
Options:
A)A)12
B)B)24
C)C)36
D)D)48
E)E)60
Rationale: According to order of operations, 12÷4×2 (division and multiplication) is done first from left to right
12÷4×2 = 3 × 2 = 6
Hence
20 - 12÷4×2 = 20 - 6 = 14
correct answer is B) 22
Answer: B
Question: The average of 11 results is 53, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)A)46
B)B)23
C)C)66
D)D)76
E)E)74
Rationale: 1 to 11 = 11 * 53 = 583
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 583 = 23
Answer:B
Answer: B
Question: Some ladies can do a piece of work in 12 days. Two times the number of such ladies will do half of that
work in :
Options:
A)6 days
B)4 days
C)12 days
D)3 days
E)2 days
Rationale: Expl : Let x ladies can do the work in 12 days. More ladies, less days (Indirect)
Less work, less days (direct)
Ladies 2x : x Work 1 : ½
2x : x , 1 : ½ : : 12 : y
:. 2x * 1*y = x* ½ *12 or y = 3
Hence the required number of days = 3
Answer: D
Answer: D
Question: The smallest number which when diminished by 3 is divisible by 21,28,36 and 45 is...
Options:
A)829
B)869
C)859
D)4320
E)427
Rationale: 427
ANSWER:E
Answer: E
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 380 km of the tour is:
Options:
A)31.11 km/hr
B)35.55 km/hr
C)71.11 km/hr
D)84.44 km/hr
E)71 km/hr
Rationale: Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 380 x 2/9 = 84.44 km/hr.
Answer : D.
Answer: D
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become eight times at the same rate?
Options:
A)12 Â½ years
B)16 Â½ years
C)18 Â½ years
D)72 Â½ years
E)12 Â½ years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
800 ---- 16 Â½ years
Answer:B
Answer: B
Question: When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction?
Options:
A)3/3
B)7/2
C)5/2
D)3/4
E)None of these
Rationale: Answer: Option E
Let the fraction be x/y.
When the numerator decreased by 25% and the denominator decreased by 20%.
(x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5
Answer: E
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 30,000, C receives:
Options:
A)s. 7,000
B)s. 7,200
C)s. 7,400
D)s. 7,700
E)s. 7,800
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
C's share = Rs. (30000 x 12/50) = Rs. 7,200.
B
Answer: B
Question: 1240 men have provisions for 12 days. If 300 more men join them, for how many days will the provisions last now?
Options:
A)12.9
B)12.0
C)9.7
D)8.6
E)12.1
Rationale: 1240*12 = 1540*x
x = 9.7
Answer:C
Answer: C
Question: All of the stocks on the over-the-counter market are designated by either a 3-letter or a 4-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Options:
A)a. 2(26^5)
B)b. 26(26^4)
C)c. 27(26^3)
D)d. 26(26^5)
E)e. 27(26^5)
Rationale: no of different stocks for 3-letter code = 26^3
no of different stocks for 4-letter code = 26^4
total = 26^3 + 26^4 = 26^3(26+1) = 27(26^3)
[Reveal]Spoiler:
Option C
Answer: C
Question: One ton has 2200 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons?
Options:
A) 1760
B) 1700
C) 2350
D) 2500
E) 8000
Rationale: 16 pounds and 4 ounces= 16*16 + 4 = 260 ounces.
13 tons = 13*2200 pound = 13*2200*16 ounces.
Hence the answer is (13*2200*16)/260 = 1760.
Answer: A.
Answer: A
Question: If m > 0 and z is m percent of y, then, in terms of m, y is what percent of z?
Options:
A)a) 100m
B)b) 1/100m
C)c) 1/m
D)d) 10,000/m
E)e) 10/m
Rationale: z= m/100 * y
So y= 100/m * z
So y= (10000/m)/100 * z
D
Answer: D
Question: The number of new words that can be formed by rearranging the letters of the word 'can' is?
Options:
A)3
B)6
C)10
D)8
E)5
Rationale: Number of words which can be formed
= 3! - 1 = 6 - 1
= 5.
Answer: E
Answer: E
Question: The largest 4 digit number exactly divisible by 88 is?
Options:
A)9935
B)9939
C)9944
D)9954
E)9960
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
C)
Answer: C
Question: Find the L.C.M of 2^3 * 3^2* 5 *7^3*11^3, 2^4 * 3^2* 5^3* 7^3*11, 2^2* 3* 5^3* 7^3*11
Options:
A)2^4 * 3^2 * 5^3 * 7^3 * 11^3
B)2^2*3^3*5^2 * 7^4 * 11
C)2^2*3^4*5^3 * 7^4 * 11
D)2^2*3^3*5^3 * 7^4 * 11^3
E)2^3*3^3*5^3 * 7^4 * 11^2
Rationale: L.C.M= product of the highest powers of 2,3,5,7 and 11=2^4 * 3^2 * 5^3 * 7^3 * 11^3
Answer (A)
Answer: A
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 20% water?
Options:
A)1.2 kg
B)1.5 kg
C)1.7 kg
D)1.6 kg
E)None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 80% (100-20).
Therefore 0.5 X Amount of flower-nectar = 0.80 X Amount of honey = 0.80 X 1 kg
Therefore amount of flower-nectar needed =
(0.80/0.51)kg=1.6 kgs
Answer : D
Answer: D
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 12 cm
Options:
A)178 cm2
B)179 cm2
C)285 cm2
D)167 cm2
E)228 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (12)
= 228 cm2
Answer: E
Answer: E
Question: P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Options:
A)7
B)4(1/2)
C)65
D)9
E)1
Rationale: Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total.
Work done by P and Q, working together in one day = 1/6 + 1/18 = 4/18 = 2/9 of the total
They would take 9/2 days = 4 (1/2) days to complete the work working together.
Answer: B
Answer: B
Question: A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
Options:
A)7/11
B)7/33
C)14/33
D)7/66
E)14/66
Rationale: The total number of ways to choose two representatives is 12C2=66.
The number of ways to choose two females is 8C2=28.
P(choosing two female representatives)=28/66=14/33
The answer is C.
Answer: C
Question: 15 Java programmers, working in a constant pace, finish a web page in 3 days. If after one day, 9 programmers quit, how many more days are needed to finish the
remainder of the job?
Options:
A)5.
B)2.
C)8.
D)4.
E)6.
Rationale: Given:
3 day's work : x
1 day's work : x/3
Given:
15 people complete the work in 3 days .
After 1 day's work (x/3), 9 people left.
Remaining work = x - x/3 =2x/3
Now ,
1 day's work of 15 persons= x/3
1 day's work of 1 person = x/45.
1 day's work of 6 persons(15-9)= 2x/15.
2x/15 work completed in 1 day.
2x/3 work completed in = 5 days
Question asks how many more days needed to complete the remaining work,therefore 5 more days needed to complete the remaining work.
Answer is A.
Answer: A
Question: If x^2 = 141, which of the following is closest to a potential value of x?
Options:
A)-127
B)-11
C)12
D)13
E)131
Rationale: Here the thing we must not forget is that X^even has two potential solutions
=> x =+- √141 => +- 12 (approx)
this value is closer to 12
Hence C is correct.
Answer: C
Question: How many two-digit whole numbers yield a remainder of 2 when divided by 12 and also yield a remainder of 2 when divided by 6?
Options:
A)None
B)Five
C)Six
D)Seven
E)Eight
Rationale: The possible number N can be written as follow:
N = Multiple of LCM(12,6) + 1st such number
N = 12x + 2
Possible values =2,26,38,50,62,86,98
Answer : 6 such 2 digit number. C.
Answer: C
Question: Of the 150 employees at company X, 50 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
Options:
A)20
B)30
C)50
D)80
E)100
Rationale: 150 employees
50 are full-time
100 have worked at company X for at least a year
20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
150-50=100 employees not full time
100-20= 80 employees not full time who worked over a year
100 employees have worked at company X for at least a year-80 employees not full time who worked over a year = 20 full-time employees of company X have worked at the company for at least a year
ans A
Answer: A
Question: Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 3, while all other numbers remain the same, what is the new average of Set S?
Options:
A)6.5
B)6.7
C)6.8
D)6.85
E)6.9
Rationale: Old set S - Total is avg * no of elements = 6.2*10 = 62
If one number is increased by 3 then total increased to 62+3=65
New avg - 65/10 = 6.5.
Hence answer is A.
Answer: A
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 22 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 10 books, how many shelves does the bookcase have?
Options:
A)8
B)6
C)7
D)5
E)4
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 8*(x-1)+10
12x-22=8(x-1)+10
4x=24
x=6. Answer B
Answer: B
Question: The average of first five prime numbers greater than 5 is?
Options:
A)13.4
B)12.26
C)12.3
D)32.8
E)32.4
Rationale: 7 + 11 + 13 + 17 + 19
= 67/5
= 13.40
Answer: A
Answer: A
Question: Find the average of all prime numbers between 30 and 50
Options:
A)35
B)39.8
C)41.2
D)50.9
E)62
Rationale: Prime numbers between 30 and 50 are 31,37,41,43,47
Required average = (31+37+41+43+47)/5 = 199/5 = 39.8
Answer is B
Answer: B
Question: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 5/8 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
Options:
A)1/3
B)1/4
C)1/5
D)1/6
E)1/8
Rationale: The fraction of homes which are termite-infested but not collapsing is 3/8*1/3 = 1/8
The answer is E.
Answer: E
Question: The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Options:
A)$400
B)$500
C)$600
D)$800
E)$900
Rationale: Let the sum be $. P.
Then,[P(1+10/100)^2 - P] = 525
->P[(11/10)^2 - 1] = 525
P = (525*100/21) = 2500
SUM = $2500
SO SI = $(2500*5*4/100) = $ 500
ANSWER : B $500
Answer: B
Question: Alex takes a loan of $8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount.
Options:
A)680
B)700
C)720
D)730
E)750
Rationale: From the details given in the problem Principle = P = $8,000 and R = 9% or 0.09 expressed as a decimal.
As the annual Interest is to be calculated, the time period T =1.
Plugging these values in the simple Interest formula,
I = P x T x R
= 8,000 x 1 x 0.09
= 720.00
Annual Interest to be paid = $720
answer :C
Answer: C
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)17%
B)18%
C)30%
D)17%
E)12%
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let the marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer: C
Answer: C
Question: 617 + 6.017 + 0.617 + 6.0017 = ?
Options:
A)6.2963
B)62.9635
C)629.6357
D)0.62963
E)None of them
Rationale: 617.00
6.017
0.617
+ 6.0017
--------
629.6357
---------
Answer is C.
Answer: C
Question: Pipe A fills a tank in 20 minutes. Pipe B can fill the same tank 4 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)2
B)3
C)4
D)5
E)6
Rationale: A's rate is 1/20 and B's rate is 1/5.
The combined rate is 1/20 + 1/5 = 1/4
The pipes will fill the tank in 4 minutes.
The answer is C.
Answer: C
Question: John invests $x at the semi-annual constant compounded rate of 2 percent and also does $15,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
Options:
A)20000
B)30000
C)40000
D)30301.5
E)50000
Rationale: A = P(1+r/n)^nt
A= total amount accrued
P = principal deposited
r = rate of interest in decimal form
n = number of times per year, interest compounded
t = time in number of years.
.
x(1+0.02/2)^2 - x = 15,000(1+0.04/4)^4 - 15,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)
=> x[(1.01)^2 - 1] = 15,000[(1.01)^4 - 1]
=> x[(1.01)^2 - 1] = 15,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides
=> x = 15,000(1.0201+1) =30301.5
Hence answer is D.
Answer: D
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
Options:
A)25
B)43
C)64
D)78
E)98
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Question: The function g(j) is defined for integers j such that if j is even, g(j) = j/2 and if j is odd, g(j) = j + 5. Given that g(g(g(g(g(j))))) = 19, how many possible values for j would satisfy this equation?
Options:
A)1
B)5
C)7
D)8
E)11
Rationale: Let me define terms:
in g(j) = R
j is argument, R is result, g() is function,
in g(g(g(g(g(j))))), g1 is inner most, g5 is outermost for identification.
From definition of function g, we can deduce that:
If Result is even then two possibilities for argument = 1 Even 1 Odd
If Result is odd then one possibility for argument = 1 Even
Since final result = 19 = Odd
Possibilities:
g1:1 Even
g2: 1*(Even,Odd ) =1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8
Ans D it is!
Answer: D
Question: 13 buckets of water fill a tank when the capacity of each bucket is 42 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 6 litres?
Options:
A)91
B)80
C)96
D)98
E)90
Rationale: Capacity of the tank = (13 Ã— 42) litre
Number of buckets required of capacity of each bucket is 17 litre = 13Ã—42/6=13Ã—7=91
Answer is A
Answer: A
Question: A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 14 white mice in the experiment, how many brown mice are in the experiment?
Options:
A)12
B)8
C)28
D)7
E)27
Rationale: Let total number of mice = M
Number of white mice = 2/3 M=14 M =21
Number of brown mice = 1/3 M = 1/3*21
=>brown mice = 7
Answer D
Answer: D
Question: During a Thanksgiving weekend, a car rental company rented seven-tenths of their vehicles, including two-fifths of the 4WDs that it had. If 40% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
Options:
A)20%
B)30%
C)40%
D)60%
E)25%
Rationale: 3/10 of all the vehicles were not rented.
(3/5)(2/5) = 6/25 of all the vehicles are 4WDs that were not rented.
(6/25) / (3/10) = 4/5 is the fraction of non-rented vehicles that were 4WDs
1 - 4/5 = 20% of non-rented vehicles were not 4WDs.
The answer is A.
Answer: A
Question: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, white and yellow. This pattern continues (red, green, blue, white and yellow) until it ends with a blue shirt. If there are more than 5 people in line, which of the following cannot be the number of people in the line?
Options:
A)27
B)38
C)53
D)63
E)78
Rationale: The correct answer should not take the form: 5x + 3. Hence, it is A
Answer: A
Question: The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?
Options:
A)0
B)2
C)2.5
D)4.67
E)10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+5)^2 & A2= (2x-3)^2
L1= x+5 & L2= 2x-3
P1 = 4( x+5) & P2=4(2x-3)
P1+P2=32
4( x+5) +4(2x-3)=32..............> X=2
Answer: B
Answer: B
Question: he number of sequences in which 10 players can throw a ball, so that the youngest player may not be the last is?
Options:
A)4328883
B)2377110
C)3265920
D)2882124
E)2782000
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 9 players. The first 6 players can throw the ball in 9p9 ways.
The required number of ways = 9(9!) = 4320
Answer:C
Answer: C
Question: 100 kg of a mixture containing milk and water in the ratio 11:5. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:2?
Options:
A)2.49kg
B)5.78kg
C)3.45kg
D)4.17kg
E)6kg
Rationale: Milk in 100kg of mix = 100*10/16 = 125/2 kg
Water in it= 100-125/2 = 75/2 kg
Let x kg of water be added to it.
(125/2)/(75/2 + x) = 3/2
x=4.17kg
Answer is D
Answer: D
Question: In how many ways can the integer 48 be expressed as a product of two different positive integers?
Options:
A)10
B)8
C)5
D)4
E)2
Rationale: Method 1: Listing all multiples since given number is small
48 = 1*48, 2*24, 3*16, 4*12, 6*8 => 5 ways
Method 2: Express given number as prime factors
48 = 6*8 = 2*3 * 2^3 = 2^4 * 3
Total number of factors = (4+1)(1+1) = 5*2 = 10
Since the given number is not a perfect square, there will be exact 5 pairs possible of the given 10 factors => 5 ways
Option C
Answer: C