divelab/Sys2Bench huggingface dataset:
Question: A greengrocer was selling apple at a penny each, chickoos at 2 for a penny and peanuts at 3
for a penny. A father spent 7p and got the same amount of each type of fruit for each of his three
children. What did each child get?
Options:
A)1 2 1
B)1 2 2
C)1 2 3
D)1 2 4
E)2 2 1
Rationale: A father spent 7p
Each child gets 1 apple=Father spent 3p on 3 apples.
Remaining 4p.
Suppose each child gets 2 chickoos=Father spent 3p on 6 chickoos
Remaining 1p
Now if each child gets 1 peanut=Father spent 1p on 3 peanuts
Ans: 1 2 1
ANSWER:A
Answer: A
Question: 8, 12, 18, 27, 40.5, (...)
Options:
A)60.75
B)30.27
C)60.9
D)30.79
E)20.5
Rationale: 8
(8×3)÷ 2 = 12
(12×3)÷ 2 = 18
(18×3)÷ 2 = 27
(27×3)÷ 2 = 40.5
(40.5×3)÷ 2 = 60.75
Answer is A
Answer: A
Question: In a series of six consecutive odd numbers, the sum of the third and fifth numbers is 50. What are the third and fifth number respectively?
Options:
A)27,31
B)31,35
C)21,25
D)23,27
E)25,29
Rationale: Let the numbers be x, x + 1, x + 3, x + 5 and x + 7.
Given (x + 3) + (x + 7) = 50
=> 2x + 10 = 50 => x = 20
The third number = x + 3 = 20 + 3 = 23.
The fifth number = x + 7 = 20 + 7 = 27.
Answer: D
Answer: D
Question: The speed of a boat in still water in 20 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:
Options:
A)9.2
B)10.2
C)9.8
D)9.6
E)10.0
Rationale: Speed downstream = (20 + 4) = 24 kmph
Time = 24 minutes =24/60 hour = 2/5 hour
Distance travelled = Time × speed =2/5×24 = 9.6 km
Answer is D.
Answer: D
Question: 14 men can complete a piece of work in 32 days. In how many days can 16 men complete that piece of work?
Options:
A)23
B)27 3/4
C)20 1/2
D)27 1/2
E)11
Rationale: 14 * 32 = 16 * x => x = 27 1/2 days
Answer:D
Answer: D
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk ?
Options:
A)34 days
B)40 days
C)46 days
D)50 days
E)None of these
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 40
Bags 40 1]::40:x
=>x∗40∗1=40∗1∗40
=>x=40
Option B
Answer: B
Question: I have 20 rupees. I bought 1, 2, 5 rupee stamps. They are different in numbers by the reason of no change, the shop keeper gives 3 one rupee stamps. So how many stamp(s) I have.
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: 5x+2y = 17
where, x and y are integer.
x = 3, y= 1 (possible)
y= 6, x = 1 (possible)
=> as they are different in number so, x is not equal to 3
one rupee coin = 3
2 two coin = 6
5 rupee coin = 1
Total = 10.
ANSWER:B
Answer: B
Question: A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 50 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
Options:
A)79
B)89
C)95
D)77.27
E)97.2
Rationale: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6
A1+A2+A3+A4+A5+A6 = 100*6 = 600
The year before , the 5 courses be B1, B2 , B3 , B4 , B5
B1+B2+B3+B4+B5 = 50*5 = 250
Student's average = (600+250)/11 = 77.27
Answer D
Answer: D
Question: If a 10 lit. mixture contains milk and water in the ratio 2:1 then, how much more mixture should be added to change the ratio to 1:2 ?
Options:
A)10 liters of water
B)15 liters of water
C)10 liters of milk
D)20 liters of water
E)20 liters of milk
Rationale: If you add the same mixture again,the ratio will still remain the same.
The question should be how much water to be added
In 10 litres, let quantity of milk = 2x and quantity of water = x
=> 2x + x = 10
=> x = 10/3 , 2x = 20/3
Let y litres of water be added to make the ratio 1:2
=> (20/3) / (10/3 + y) = 1 / 2
=> 40/3 = 10/3 + y
=> y = 10 liters
Therefore,10 liters of water to be added.
ANSWER:A
Answer: A
Question: How many four letter combinations can be formed using the letters of the word TRIPS?
Options:
A)12
B)24
C)120
D)240
E)300
Rationale: The number of letters in the given word is five.
The number of four letter combinations that can be formed using these five letters is
= 5 * 4 * 3 * 2 = 120.
Answer: C
Answer: C
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $65,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
Options:
A)$10,000
B)$33,000
C)$12,000
D)$12,800
E)$13,200
Rationale: 1 machine of type B will cost: 20% down payment of 65,000 = 13,000plusremaining sum (65,000-13,000=52,000) with 40% of finance charges 52,000*1.4=72,800 --> 13,000+72,800=85,800;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 85,800 - 52,800 = 33,000.
Answer: B.
Answer: B
Question: Andy has 20 pairs of matched gloves. If he loses 14 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
Options:
A)9
B)11
C)13
D)14
E)15
Rationale: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched of pairs
Case1: If 14 gloves are gone the maximum probability of losing maximum gloves is 14 pairs of gloves out of 20. This means i m having 6 pairs of gloves. [Minimum number of gloves i can have is 6 pairs]
Case2: If 14 gloves are gone the maximum probability of losing minimum gloves is 14/2 = 7 means i can lose 7 glove. in this scenario i will be having 13 gloves.
Hence10 < Available Glove Pair < 14
any given time I cant possess 14 glove pair for the above mentioned scenario. And thats the answer. D.
Answer: D
Question: Out of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 45 percent of the total number of employees work in research, how many male employees do NOT work in research?
Options:
A) 238
B) 480
C) 392
D) 208
E) 88
Rationale: total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =45% =450
Total male employees =48%=480
male employees working in research =450-208=242
male employees not working in research =480-242=238
Answer A
Answer: A
Question: Which is the middle even number between 12 and 24?
Options:
A)24
B)36
C)42
D)8
E)19
Rationale: 12+x = 24-x
2 x = 14
X = 7
Now 12+x = 19
ANSWER:E
Answer: E
Question: Ten percent of Ram's monthly salary is equal to eight percent of Shyam's monthly salary. Shyam's monthly salary is twice Abhinav's monthly salary. If Abhinav's annual salary is Rs. 1.92 lakhs, find Ram's monthly salary?
Options:
A)Rs. 18000
B)Rs. 20000
C)Rs. 25600
D)Rs. 32000
E)None of these
Rationale: Let the monthly salaries of Ram and Shyam be Rs. r and Rs. s respectively.
10/100 r = 8/100 s
r = 4/5 s
Monthly salary of Abhinav = (1.92 lakhs)/12 = Rs. 0.16 lakhs
s = 2(0.16 lakhs) = 0.32 lakhs
r = 4/5(0.32 lakhs) = Rs. 25600
ANSWER:C
Answer: C
Question: A box contains five bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
Options:
A)256/625
B)1/6
C)369/625
D)1/5
E)4/5
Rationale: Required probability
= 1 - 256/625
= 369/625
Answer: C
Answer: C
Question: In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (-1, 0), (7, 4), and (7, -4)?
Options:
A)29
B)30
C)31
D)32
E)33
Rationale: The triangle is symmetric about the x-axis.
The part above the x-axis forms a triangle with a base of 8 and a height of 4.
The area of this part is (1/2)(8)(4).
We can double this to find the area of the whole triangle.
The total area is (2)(1/2)(8)(4) = 32.
The answer is D.
Answer: D
Question: The "factor count" of an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest?
Options:
A)60
B)61
C)62
D)63
E)64
Rationale: (A)	60 = 2^2*3*5 --> factor count = 3;
(B)	61 = prime --> factor count = 1;
(C)	62 = 2*31 --> factor count = 2;
(D)	63 = 3^2*7 --> factor count = 2;
(E)	64 = 2^6 --> factor count = 1.
Answer: A.
Answer: A
Question: A bag contains 80 black balls and 10 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)2/5
B)5/7
C)1/9
D)1/4
E)1/3
Rationale: Total number of balls = 80+10 = 90
no. of white balls = 10
probability of drawing a white ball = 10/90 = 1/9
Answer is C
Answer: C
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 45 years, was replaced by a new person. Find the age of the new person?
Options:
A)18
B)56
C)12
D)15
E)14
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 45 + Q
=> Q = 15
Answer:D
Answer: D
Question: Find out the wrong term in the series 2, 5, 10, 50, 500, 5000
Options:
A)5000
B)3877
C)6777
D)2892
E)2881
Rationale: Explanation:
Each term of the series is the product of the preceding two terms
So, 5000 is wrong and it must be replaced by (500*50) = 25000
Answer: A) 5000
Answer: A
Question: A reduction of 10% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)s.42
B)s.46
C)s.40
D)s.41
E)s.16
Rationale: 800*(10/100) = 80 ---- 5
? ---- 1 => Rs.16
Answer: E
Answer: E
Question: How many positive integers less than 248 are multiple of 4 but NOT multiples of 6?
Options:
A)20
B)41
C)42
D)53
E)64
Rationale: 244/4=61
Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0
240/12=20
61-20=41
Answer: B
Answer: B
Question: How many two-digit numbers yield a remainder of 3 when divided by both 4 and 14?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Easier to start with numbers that are of the form 14p+3 ---> 17,31,45,59,73,87.
Out of these 3 (31,59,87) are also of the form 4q+3. Thus 3 is the answer. D is the correct answer.
Answer: D
Question: If 25 toys cost Rs, 234, what do 35 toys cost?
Options:
A)327.6
B)564.6
C)546.6
D)654.6
E)None of them
Rationale: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
x=(35 X 234)/25 =327.60
Answer is A
Answer: A
Question: A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction X of the selected films are in color?
Options:
A)1/130
B)1/5
C)3/13
D)10/13
E)30/31
Rationale: It's y/xpercentnot y/x.
If x=20 and y=10. Then:
20x=400 black-and-white films;
6y=60 color films.
y/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.
Color films thus compose X= 60/62=30/31 of the selected films.
Answer: E.
Answer: E
Question: The average age of a husband, wife and their child 2 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Options:
A)19.2 years
B)28.5 years
C)16.4 years
D)15.6 years
E)14.2 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/2
= 28.5 years.
Answer:B
Answer: B
Question: In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee?
Options:
A)38
B)40
C)42
D)46
E)49
Rationale: 1W 2M 2W 1M 3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
Atleast one women = total - with out women
Atleast one women = 56 - 10 = 46
D)
Answer: D
Question: Which of the following fractions is smaller than 17/50?
Options:
A)2/5
B)11/34
C)43/99
D)8/21
E)9/20
Rationale: Answer B
17/50=0.34
11/34=0.323529 which is 0.01647 smaller than 0.34
Answer: B
Question: If x is a positive integer, and two sides of a certain triangle have lengths 30 and 45 respectively, which of the following could be the length of the third side of the triangle?
I. 45
II. 75
III. 145
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II and III
Rationale: Following the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides:
Difference of other 2 sides < any side < sum of other two sides. Let the third side of triangle be AB.
So, 45 - 30 < AB < 45+30,
and 15 < AB < 75
Check if any of the answers are between 15 and 75.
I: 45 ; could be a possible value.
II: 75 ; could not be a possible value.
III: 145; could not be a possible value.
Answer :A
Answer: A
Question: If 3x - 3x-1 = 18, then the value of xx is
Options:
A)3
B)8
C)27
D)36
E)NOne
Rationale: Sol.
3x - 3x-1 = 18
⇔ 3x-1 (3 - 1) = 18
⇔ 3x-1 = 9
⇔ 32
⇔ x-1 = 2
⇔ x = 3.
∴ xx = 33 = 27.
Answer C
Answer: C
Question: On day one, a store sold 96 pens. On each of the next d days, the company sold 44 pens. If the average daily sales of pens over this time period (including day one) is 48 pens, what is the value of d?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: 96 + 44d = 48(d+1).
4d = 48.
d = 12.
The answer is D.
Answer: D
Question: 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8.
What is half of that number?
Options:
A)305
B)315
C)345
D)325
E)335
Rationale: Let the number be x. then 4/15 of 5/7 of x-4/9 of 2/5 of x=84/21x-8/45x=8
(4/21-8/45)x=8(60-56)/315x=84/315x=8
x=(8*315)/4=6301/2x=315
Hence required number = 315
Answer is B.
Answer: B
Question: A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water?
Options:
A)22
B)37
C)32
D)27
E)18
Rationale: US = 25
DS = 39
M = (39 + 25)/2 = 32
Answer:C
Answer: C
Question: Tom, Mary and Sue each wrote an essay for their English class. Together, the three of them wrote a total of 650 pages. Mary and Sue wrote a total of 450 pages together, and Mary and Tom wrote a total of 350 pages together. How many pages did Mary write by herself?
Options:
A)200
B)250
C)150
D)300
E)350
Rationale: Tom + Mary + Sue = 650 pages
Mary + Sue = 450 pages << Plug this into the original formula to get Tom's total
Mary + Tom = 350 pages << Plug this into the original formula to get Sue's total
(Mary + Sue) + Tom = 650 pages >> 450 + Tom = 650 >> Subtract 450 from each side >> Tom = 200
(Tom + Mary) + Sue = 650 pages >> 350 + Sue = 650 >> Subtract 350 from each side >> Sue = 300
Now plug in Tom & Sue into the original formula.
200 + Mary + 300 = 650 <<Subtract 200 and 300 from each side
Mary = 150 pages
Answer: C
Answer: C
Question: In a rectangular coordinate system, points O (2,2), P (2,12), and Q (10,2) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?
Options:
A)(5,6)
B)(8,7)
C)(5,8)
D)(6,6)
E)(6,7)
Rationale: All points equidistant from O and Q lie on the line x = 6, so the fire station should lie on this line.
All points equidistant from O and P lie on the line y = 7, so the fire station should lie on this line.
These two intersect at (6,7) and that will be the point equidistant from all 3 points.
The answer is E.
Answer: E
Question: The perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm. What is the area of the triangle?
Options:
A)128 cm2
B)36.0 cm2
C)105 cm2
D)25 cm2
E)135 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 5.0 * 42/2
= 105 cm2
Answer: C
Answer: C
Question: During a clearance sale, a retailer discounted the original price of its TVs by 21% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
Options:
A)40%
B)45%
C)55%
D)60%
E)63.5%
Rationale: VERITAS PREPOFFICIAL SOLUTION:
D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 63.5%.
E
Answer: E
Question: How many three digit numbers are there which are equal to 3434 times the sum of their digits?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: If the product is written abcabc in decimal, then we have
100a+10b+c=34(a+b+c)
100a+10b+c=34(a+b+c)
(a,b,c<10,a≠0a,b,c<10,a≠0). Thus
66a−33c=24b
66a−33c=24b
and, since 1111 divides the left-hand side, 11|b11|b. Since b<10b<10, b=0b=0. We're left with two requirements: 2a=c2a=c and 34|a0c1034|a0c10. Testing the possibilities afforded by 2a=c2a=c, we see 102102 is divisible by 3434, so all its multiples are answers also, and the answer is 4.
Answer is A
Answer: A
Question: The perimeter of a square is 36 m. Find the area of the square.
Options:
A)81 mÂ².
B)84 mÂ².
C)86 mÂ².
D)169 mÂ².
E)273 mÂ².
Rationale: Perimeter of square = 36 m
But perimeter of square = 4 Ã— side
Therefore, 4 Ã— side = 36 m
Therefore, side= 36/4 m = 9m
Now, the area of the square = (side Ã— side)
Therefore, area of the square = 9 Ã— 9 mÂ² = 81 mÂ².
ANSWER : OPTION A
Answer: A
Question: Of 30 applicants for a j ob, 14 had at least 4 years of exper, 18 had degrees, and 3 had less than 4 years exper and did not have a degree, how many applicants had at least 4 years exper and a degree?
Options:
A)a)14
B)b)13
C)c)9
D)d)7
E)e)5
Rationale: Answer is E. Here is how:
The quickest way is to setup a matrix and work through the given values in the question.
For all such problems, set up a matrix with number of columns and rows corresponding to the divisions mentioned in the question stem.
Degrees and Experience
> 4 yrs Exp< 4 yrs ExpTotal
Degree5Required Value1318Given
No Degree9312
Total14Given1630Given answer is E
Answer: E
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?
Options:
A)1/12
B)1/18
C)1/19
D)1/16
E)1/11
Rationale: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer: A
Answer: A
Question: The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m, find out the area of the field.
Options:
A)37500
B)38000
C)38500
D)39000
E)39500
Rationale: Given that breadth of the rectangular field is 60% of its length.
⇒b=60l100=3l5
perimeter of the field =800 m
⇒2(l+b)=800⇒2(l+3l5)=800⇒l+3l5=400⇒8l5=400⇒l5=50⇒l=5×50=250 m
b=3l5=3×2505=3×50=150 m
Area =lb=250×150=37500 m2
Answer is A.
Answer: A
Question: Last year, for every 100 million vehicles that traveled on a certain highway, 75 vehicles were involved in accidents. If 6 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
Options:
A)2500
B)4500
C)3500
D)4000
E)1300
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 75 accidents as 6 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 6,000 million rather than 6 billion. Creating a proportion we have:
100/75 = 6,000/x
Cross multiplying gives us:
100x = 6,000 * 75
x = 60 * 75 = 4500
Answer : B
Answer: B
Question: Find the area, diameter = 9 m.
Options:
A)63.00 square meter
B)63.64 square meter
C)63.08 square meter
D)63.24 square meter
E)63.43 square meter
Rationale: Diameter = 9 meter.
Radius = diameter/2.
= 9/2.
= 4.5 meter.
Area of a circle = Ï€r2.
Here, pi (Ï€) = 3.14 meter, radius (r) = 4.5.
Area of a circle = 3.14 Ã— 4.5 Ã— 4.5.
= 3.14 Ã— 20.25.
= 63.64 m2. ANSWER : B
Answer: B
Question: Find the next number in the sequence
1, 2, 6, 21, 88, __?
Options:
A)134
B)234
C)445
D)345
E)678
Rationale: C
445
2=(1+1)1
6=(2+1)2
21=(6+1)3
88=(21+1)4
So 445=(88+1)5
Answer: C
Question: Two trains A and B start simultaneously in the opposite direction from two points A and B arrive at their destinations 9 and 4 hours respectively after their meeting each other. At what rate dose the second train B travels if the first train travels at 80 km per hour. Option
Options:
A)60 km/h
B)100 km/h
C)120 km/h
D)80 km/h
E)90 km/h
Rationale: If two trains (or bodies) start at the same time from points A and B towards each other and after
crossing they take a and b sec in reaching B and A respectively, then
(A's speed) : (B’s speed) = √b:√a.
hence the answer 120 km/hr
ANSWER:C
Answer: C
Question: 0.004 × 0.5 = ?
Options:
A)None of these
B)0.02
C)0.002
D)0.0002
E)2
Rationale: Explanation :
0.004 × 0.5 = 0.002. Answer : Option C
Answer: C
Question: Statement : All the organised persons find time for rest. Sunita, in-spite of her busy schedule, finds time for rest.
Conclusions :
I. Sunita is an organised person.
II. Sunita is an industrious person.
Options:
A) I only
B) II only
C) I and II only
D) I and III only
E) II and III only
Rationale: Sunita has a busy schedule. This means that she is industrious. But still she finds the time for rest. This means that she is an organised person.
So both conclusions follow.
Answer D)
Answer: D
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
Options:
A)707
B)704
C)709
D)705
E)701
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm
= 704 m
Answer:B
Answer: B
Question: Line Q has the equation 5y – 3x = 60. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)
Options:
A)35
B)40
C)45
D)50
E)55
Rationale: 5y - 3x = 60 and so y = 3x/5 + 12
When x = 0, then y = 12.
When y = 0, then x = -20
The slope is 3/5, so the slope of line S is -5/3.
Through the point (-20, 0), 0 = -5(-20)/3 + c
The y-intercept is c = -100/3 < -33.
Thus the perpendicular line S can have y-intercepts from -33 up to 11.
The number of possible lines is 33 + 11 + 1 = 45
The answer is C.
Answer: C
Question: In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 7 women?
Options:
A)A)84
B)B)15
C)C)20
D)D)18
E)E)21
Rationale: Required number of ways = 4C3*7C2 = 4*21 = 84
Answer is A
Answer: A
Question: If 5x = 6y and xy ≠ 0, what is the ratio of 1/4*x to 1/6*y ?
Options:
A) 25/6
B) 36/25
C) 9/5
D) 5/6
E) 25/36
Rationale: 5x = 6y => x/y = 6/5
1/4*x to 1/6*y = x/y * 3/2 = (6/5)*(3/2)=9/5
Ans: C
Answer: C
Question: 15 girls can complete a rangoli in 12 days, and 10 boys can complete the same work in 15 days. To complete the work earlier 10 boys and 15 girls are employed, in how many days will this work get completed?
Options:
A)6
B)7
C)6.5
D)6 2/3
E)6 1/4
Rationale: Work done by 15 girls per day =1/12
Work done by 10 boys per day = 1/15
Work done by 15 girls and 10 boys per day=1/12+1/15=3/20=6 2/3
10 boys and 15 girls will complete the work in =6 2/3 days
D
Answer: D
Question: Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 80% of the cost over $600. Plan Q requires the insured to pay the initial $300, but then pays 60% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A)$1200
B)$1500
C)$1800
D)$2100
E)$2400
Rationale: 0.8(x-600)=0.6(x-300)
0.2x=480-180
x=1500
The answer is B.
Answer: B