divelab/Sys2Bench huggingface dataset:
Question: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?
Options:
A). 1/2
B)2
C)1/4
D)3
E)3/4
Rationale: Soln:-
Added the line BE (the required line that divides the given parallelogram into 2 identical quadrilaterals).
Careful observation reveals that slope of the diagonal AD = (1-0)/(3-1) = 0.5. Thus the slope of line BE should be < slope of AD
Only option C is < 0.5 and is thus the correct answer.
Answer: C
Question: If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)288
B)162
C)189
D)168
E)122
Rationale: 14 m/s = 14 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 14 * 18/5 * 15/4 km = 189 km.
Answer: C
Answer: C
Question: For positive integers n, the integer part of the nth term of sequence D equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, D_1 = 1.2345678…, while D_2 = 2.4681012… The sum of the first seven terms of sequence D is between:
Options:
A)28 and 29
B)29 and 30
C)30 and 31
D)31 and 32
E)32 and 33
Rationale: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
D_1 = 1.23…
D_2 = 2.46…
D_3 = 3.69…
D_4 = 4.812…
D_5 = 5.10…
D_6 = 6.12…
D_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
Answer: C
Question: An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of
Options:
A)580 Kmph
B)550 Kmph
C)540 Kmph
D)530 Kmph
E)520 kmph
Rationale: Explanation:
Speed of aeroplane = 420 Kmph
Distance travelled in 6 hours
= 420 * 6 = 2520 Km
Speed of aeroplane to acver 2520 Km in 14/3
= 2520*3/14 = 540 Km
Answer: Option C
Answer: C
Question: price of apple mobile is double than samsung and triple than oppo.the mean off all three phone's price is 25000.what is price of samsung.
Options:
A)21,200.20
B)22,000
C)20,454.54
D)23,300.33
E)24,000
Rationale: solution
let the price of oppo is x,then price of apple 3x and price of samsung 1.5x
(x+3x+1.5x)/3=25000
5.5x=75000
x=75000/5.5=13,636.36
Samsung price=1.5x=20,454.54
answer C
Answer: C
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)76 m2
B)10 m2
C)27 m2
D)18 m2
E)17 m2
Rationale: 1/2 * 4 * 5 = 10 m2
Answer:B
Answer: B
Question: an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -w and a*w=0, then w=?
Options:
A)a) -a
B)b) -1/a
C)c) 1/a
D)d)0
E)e)a
Rationale: If a*w=0 and a=-w then a-w = o of a=w, so answer E
Answer: E
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 520 kms in 4 hours, then the speed of the first train is:
Options:
A)89.25 km/hr.
B)37.25 km/hr.
C)90.25 km/hr.
D)113.75 km/hr.
E)96.25 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (520/4) = 130
x = (130/8) = 16.25
Hence, speed of first bullet train = (7 x 16.25) km/hr = 113.75 km/hr.
D
Answer: D
Question: Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents Z watch all of the shows?
Options:
A) 150
B) 108
C) 42
D) 21
E) -21
Rationale: OA is D.
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is Z =3.5% of 600, is 21. D is the correct answer
Answer: D
Question: If a and b are both negative and ab < b^2, which of the following must be true?
Options:
A)a < b < a^2 < b^2
B)a < b < b^2 < a^2
C)b < a < a^2 < b^2
D)a^2 < b^2 < b < a
E)b^2 < a^2 < b < a
Rationale: Because ab < b^2 and both are negative, I thought a < b. So I crossed off answers c), d), and e).
And because a < b , a^2 < b^2
ans C
Answer: C
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 17%, then the cost price of the article is:
Options:
A)500
B)334
C)555
D)664
E)526
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/117 = Rs. 526
Answer: Option E
Answer: E
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Options:
A)12.9
B)12.0
C)12.5
D)12.2
E)12.1
Rationale: 1000*15 = 1200*x
x = 12.5
Answer:C
Answer: C
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)29
B)37
C)54
D)42
E)60
Rationale: After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
125 : 150 :: 35 : x
125 * x = 150 x 35
x =	(150 x 35)/125
x = 42.
Answer is D.
Answer: D
Question: The average age of students of a class is 15.7 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
Options:
A)3:7
B)7:3
C)2:5
D)2:1
E)2:4
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.7
= (16.4 - 15.7)k = (15.7 - 15.4)
= k = 0.3/0.7 = 3/7
Required ratio = 3/7 : 1 = 3:7.
Answer:A
Answer: A
Question: When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 731 more than 4times the middle integer. Find the numbers?
Options:
A)650
B)731
C)698
D)710
E)729
Rationale: x + 4 (x + 4) = 731 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 731 + 4 x + 8
x = 723
x + 2 = 725
x + 4 = 727
Check: the smallest is added to four times the largest
723 + 4 * 727 = 3631
four times the middle
4 * 725 = 2900
3631 is more than 2900 by
3631 - 2900 = 731
B
Answer: B
Question: Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
Options:
A)27
B)26
C)25
D)24
E)23
Rationale: Solution:
We know that the average value is 22 therefore (a+b+c)/3 = 22
so a+b+c = 66
and b = a + 13
therefore a + (a + 13) + c = 66
The least value of c is when c = b
so take c = a + 13
hence, a + (a + 13) + (a + 13) = 66
i.e., a = 40/3 a non integer therefore c is not equal to b
so take c = b+1 therefore c = a+14
a + (a + 13) + (a + 14) = 66
i.e., a= 39/3 = 13
hence, a = 13, b = 26, and c = 27
Answer: A
Answer: A
Question: All of the stocks on the over-the-counter market are designated by either a 5-letter or a 5-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)2(26^5)
B)26(26^4)
C)27(26^4)
D)26(26^5)
E)27(26^5)
Rationale: Number of 4-letter codes: 26 * 26 * 26 * 26 * 26= 26^5
Number of 5-letter codes: 26 * 26 * 26 * 26 * 26 = 26^5
Total Number of codes: 26^5 + 26^5 = 2*(26^5)
Therefore, the answer isA: 2*(26^5).
Answer: A
Question: A pineapple costs Rs 9 each and a watermelon costs Rs. 6 each. If I spend Rs 51 on total what is the number of pineapple I purchased?
Options:
A)6
B)7
C)5
D)3
E)2
Rationale: 5*9 +6 = 51
5 pineapples
Answer : C
Answer: C
Question: Find the odd man out
3, 7, 15, 27, 63, 127, 255
Options:
A)7
B)15
C)27
D)63
E)54
Rationale: 1*2+1 = 3
3*2+1 = 7
7*2+1 = 15
15*2+1 = 31
31*2+1 = 63
63*2+1 = 127
127*2+1= 255
ANSWER:C
Answer: C
Question: How many possible ways can 4 girls (Rebecca, Kate, Ashley) go on a date with 4 boys (Peter, Kyle, Sam)?
Options:
A) 3
B) 4
C) 5
D) 6
E) 24
Rationale: Any one girl can go with 4 boys.
2nd girl can go with remaining 3 boys
3nd girl can go with remaining 2 boys
and 3rd girl can go with remaining 1 boy
4! i.e 24 (E) is the answer
Answer: E
Question: The least number, which when divided by 12, 31, 20 and 54 leaves in each case a remainder of 8 is:
Options:
A)448
B)488
C)16748
D)548
E)560
Rationale: Required number = (L.C.M. of 12, 31, 20, 54) + 8
= 16740+ 8
= 16748.
answer :C
Answer: C
Question: One out of every 100 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
Options:
A)2,000
B)5,000
C)10,000
D)50,000
E)52,000
Rationale: 20 broken glasses indicates that 10*10= 100 defected bulbs are present.
100 defected bulbs indicates that 100*100= 10,000 light bulbs are present.
C is the answer
Answer: C
Question: If a job is complete by a and b in z days,b and c in x days and a and c in y days. In how many days that a,b and c can be work simultaneously?
Options:
A)2(xyz/xy+yz+xz)
B)xyz/xy+yz+xz
C)(xy+yz+xz)/xyz
D)cannot be determined
E)2(xy+yz+xz)/xyz
Rationale: Option A is answer.
one day work of a+b,b+c and c+a is 1/z,1/x and 1/y.
That is , 2(a+b+c)=(yz+xz+xy)/xyz.
a+b+c=(yz+xz+xy)/2xyz.(one day work).
Total work done by a,b and c is 2xyz/(xy+yz+xz).
Answer: A
Question: A plane flies 660 km with the wind and 540 km against the wind in the same length of time. If the speed of the wind is 20 km/h, what is the speed of the plane in still air?
Options:
A)160 km/h
B)180 km/h
C)200 km/h
D)220 km/h
E)240 km/h
Rationale: The speed of the plane in still air = x km/h
The speed of the wind is 20 km/h
Speed with the wind = (x + 20) km/h
Speed against the wind = (x â€“ 20) km/h
Time = Distance/ Speed
660 / (x+20) = 540 / (x-20)
660(x-20) = 540(x+20)
66x - 1320 = 54x + 1080
12x = 2400
x = 200
Therefore, the speed of the plane in still air is 200 km/h.
The answer is C.
Answer: C
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 2 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Options:
A)480
B)240
C)289
D)270
E)927
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 2 = 240
Answer: B
Answer: B
Question: A man sells a horse for Rs.1400 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)2270
B)2990
C)1540
D)8600
E)7710
Rationale: CP = SP + 1CP = SP - g
1400 + x = 980 - 2x
3x = 420 => x = 140
CP = 1400 + 140 = 1540
Answer: C
Answer: C
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
Options:
A)176
B)500
C)278
D)270
E)279
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer:B
Answer: B
Question: A train running at the speed of 90 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)298 m
B)225 m
C)208 m
D)988 m
E)299 m
Rationale: Speed = 90 * 5/18 =25/1 m/sec
Length of the train = speed * time = 25 * 9
= 225 m
Answer:B
Answer: B
Question: What is the probability of having 53 Fridays in an ordinary year
Options:
A)1/5
B)1/6
C)1/7
D)1/8
E)1/9
Rationale: 1/7 because 53 friday in ordinary year then 53*7=371 (53/371=1/7)
ANSWER:C
Answer: C
Question: Two girls started running simultaneously around a circular track of length 1200 m from the same point at speeds of 30 km/hr and 50 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)50
B)51
C)52
D)53
E)54
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 1200 / (30 + 50)5/18 = 1200* 18 / 80 * 5 = 54 seconds.
Answer:E
Answer: E
Question: Two whole numbers whose sum is 72 cannot be in the ratio
Options:
A)3 : 4
B)3 : 5
C)4 : 5
D)5 : 7
E)None
Rationale: Sol.
The sum of the ratio terms must divide 72. So, the ratio
cannot be 3 : 4.
Answer A
Answer: A
Question: What is the are of an equilateral triangle of side 16 cm?
Options:
A)66√3 cm2
B)74√3 cm2
C)64√3 cm2
D)64√5 cm2
E)14√3 cm2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;
Answer:D
Answer: D
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length.
Options:
A)22
B)88
C)27
D)40
E)11
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500∗2/25=40seconds
Answer: C
Answer: C
Question: 3/8 of 168 * 15 / 5 + X = 549 / 9 + 275
Options:
A)147
B)149
C)268
D)2696
E)2976
Rationale: Explanation:
Let 3/8 of 168 * 15 / 5 + X = 549 / 9 + 275
Then, 63 * 15 / 5 + X = 61 + 275
63 * 3 + X = 336
189 + X = 336
X = 147
ANSWER: A
Answer: A
Question: The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive?
Options:
A)2.5
B)3.00
C)3.25
D)3.75
E)4.0
Rationale: For first 0.25 miles 34 cents.
So the person is left with 1.24-0.34 = 0.9
So the person can travel next (90/6) times 1/5 miles
i.e 15 *1/5 miles = 3 miles.
SO total distance is 3 + 0.25 = 3.25 miles(C)
Answer: C
Question: In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
Options:
A)4! x 9!
B)4! x 2!
C)4! x 5!
D)4! x 6!
E)7! x 9!
Rationale: Explanation:
The word EDUCATION is a 9 letter word, with none of the letters repeating.
The vowels occupy 3rd,5th,7th and 8th position in the word and the remaining 5 positions are occupied by consonants
As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the afore mentioned 4 places and the consonants can occupy1st,2nd,4th,6th and 9th positions.
The 4 vowels can be arranged in the 3rd,5th,7th and 8th position in 4! Ways.
Similarly, the 5 consonants can be arranged in1st,2nd,4th,6th and 9th position in5! Ways.
Hence, the total number of ways = 4! × 5!
Answer: C) 4! x 5!
Answer: C
Question: The average of first 6 prime numbers is?
Options:
A)10.11
B)11.11
C)12.11
D)6.83
E)14.11
Rationale: Sum of 6 prime no. = 41
Average = 41/6 = 6.83
ANSWER: D
Answer: D
Question: A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)177 m
B)176 m
C)450 m
D)187 m
E)186 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 50 = 15
x + 300 = 750
x = 450 m.
Answer: C
Answer: C
Question: X, Y and Z can do a work in 6 , 9 and 10 days respectively. They completed the work and got Rs.775. What is the share of Y?
Options:
A)250
B)240
C)260
D)230
E)245
Rationale: The ratio of their working rates = 1/6 : 1/9 : 1/10 = 15 : 10 : 6.
Since, they work together, the share of y
= 10/31 * 775 = Rs.250
Answer: A
Answer: A
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
A)1/6
B)1/3
C)1/5
D)1/1
E)1/2
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer: C
Answer: C
Question: A certain bus driver is paid a regular rate of $18 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
Options:
A)36
B)40
C)44
D)48
E)52
Rationale: For 40 hrs = 40*18=720
Excess = 976-720=252
For extra hours =.75(18)=13.5+18=31.5
Number of extra hrs =252/31.5=8
Total hrs =40+8=48
Answer D 48
Answer: D
Question: In a group of cows and chickens, the number of legs was 16 more than twice the number of heads. The number of cows was:
Options:
A)8
B)7
C)10
D)12
E)14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 16 more than twice the number of heads.
Therefore, 2 × (x + y) + 16 = 4x + 2y.
or, 2x + 2y + 16 = 4x + 2y.
or, 2x + 16 = 4x [subtracting 2y from both sides].
or, 16 = 4x – 2x [subtracting 2x from both sides].
or, 16 = 2x.
or, x = 8 [dividing by 2 on both sides].
Therefore, the number of cows = 7.
Correct Answer:A)8
Answer: A
Question: Calculate the cost of e yards of cloth given that the cost of f yards of said cloth is g rupees?
Options:
A)Rs.(e*f)
B)Rs.(g*f)
C)Rs.(eg/f)
D)Rs.(g/f)
E)Rs.(e/f)
Rationale: Cost of f yards = Rs. g.
Cost of 1 yard = Rs.	g/f
Cost of e yards = Rs.(g/f)* e= Rs.(eg/f)
Answer is C.
Answer: C
Question: Calculate the area of a triangle, if the sides are 13 cm, 12 cm and 5 cm, what is its area?
Options:
A)36 cm2
B)35 cm2
C)30 cm2
D)32 cm2
E)31 cm2
Rationale: The triangle with sides 13 cm, 12 cm and 5 cm is right angled, where the hypotenuse is 13 cm.
Area of the triangle = 1/2 * 12 * 5 = 30 cm2
Answer: C
Answer: C
Question: There are 100 students in a class. If 14% are absent on a particular day, find the number of students present in the class.
Options:
A)43
B)36
C)86
D)129
E)11
Rationale: Number of students absent on a particular day = 14 % of 100
i.e., 14/100 × 100 = 14
Therefore, the number of students present = 100 - 14 = 86 students.
Answer:C
Answer: C
Question: If x/6 and x/15 are integers, then x must be divisible by -
Options:
A)12
B)18
C)30
D)45
E)60
Rationale: Factors of 6 2 and 3
factors of 15 are 3 and 5
So number is 2*3*5 = 30
ANSWER:C
Answer: C
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 140 units?
Options:
A)50 hours
B)40 hours
C)17.5 hours
D)12 hours
E)8 hours
Rationale: Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by each machine every 10 hours
Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...
10 hours/4 units = 2.5 hours per unit when 1 machine is working.
The prompt asks us how long would it take 20 machines to produce 140 units.
If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 140 units is '7 times' 20, we need '7 times' more TIME.
(2.5 hours)(7 times) = 17.5 hours
Final Answer:
[Reveal]Spoiler:
C
Answer: C
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $16. If the shop keeper has a order of 200 articles, how much profit he will get?
Options:
A)A)200
B)B)2000
C)C)1500
D)D)1200
E)E)600
Rationale: Total money after selling articles = 200*16 = 3200
cost price = 200*10 = 2000
profit = 1200
correct option is D
Answer: D
Question: There are 50 people in a certain community who belong to the local golf club, tennis club or both clubs. If 1 as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
Options:
A)1) 4
B)2) 7
C)3) 17
D)4) 21
E)5) 27
Rationale: x -> Golf Club
x -> Tennis Club
y -> both
x+x-y = 50
2x - y =50
multiples of 2 greater than 50
52
54-4=50
IMO (A)
Answer: A
Question: A customer pays 65 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
Options:
A)A)$50
B)B)$60
C)C)$70
D)D)$85
E)E)$90
Rationale: Let x be the original price.
x - 20 = 65
x - 20 + 20 = 65 + 20
x + 0 = 85
x = 85
correct answer is D)$85
Answer: D
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)1642
B)1640
C)1632
D)2789
E)6386
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025
=1640
Answer:B
Answer: B
Question: The average of six number is 3.95. The average of two of them is 3.4, while the average of the other two is 3.62. what is the average of the remaining two number ?
Options:
A)4.5
B)4.6
C)4.7
D)4.83
E)None of these
Rationale: solution:
Sum of the remaining two numbers = (3.95 × 6) - [(3.4 × 2) + (3.62 ×2)]
=23.70 -(6.8 + 7.24) = 23.70 - 14.04 = 9.66.
∴ Required average =9.66/2 = 4.83 Answer D
Answer: D
Question: A began business with Rs.27000 and was joined afterwards by B with Rs.54000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)9
B)6
C)7
D)8
E)2
Rationale: 27*12 : 54*x = 2: 1
x = 3
12 -3 = 9
Answer: A
Answer: A
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 6w widgets.
Options:
A)4
B)36
C)8
D)10
E)12
Rationale: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 36 days to doing 6w widgets.
Answer : B
Answer: B
Question: james works in a bakery. He made cookies that cost $2 and made $200. How many customer did he have?
Options:
A)200 customers
B)85 customers
C)250 customers
D)100customers
E)170 customers
Rationale: A cookie costs $2 adding another one is $4. 200 divided by 3 is 50 x 2 is 100. He had 100 customers. The correct answer is D.
Answer: D
Question: The product of a and b is equal to 11 more than twice the sum of a and b. If b = 7, what is the value of b - a?
Options:
A)2
B)5
C)7
D)24
E)35
Rationale: Given: ab = 2(a + b) + 11 and b = 7
Hence 7a = 2a + 14 + 11
5a = 25, a = 5
(A potential trap. Do not get excited here. We need to find b - a, not a)
b - a = 7 - 5 = 2
Correct Option: A
Answer: A
Question: In year Y imported machine tools accounted for 20 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
Options:
A)15x
B)13x
C)12.5x
D)14x
E)14.5x
Rationale: Sales of imported tools = 20% of the total sales = 0.20*{total} = {total}/5;
Sales of Japanese tools = 40% of the sales of imported tools = 2/5*{total}/5 = 2{total}/25
Since the sales of of Japanese tools was x, then 2{total}/25 = x -->2{total} = 25 x
{total} = 25x/2 =12.5 x
Answer: C
Answer: C
Question: In how many ways can the integer 84 be expressed as a product of two different positive integers?
Options:
A)10
B)8
C)5
D)4
E)2
Rationale: 84=(2^2)*3*7
Since 84 is not a perfect square, no of ways=4
Answer D
Answer: D