divelab/Sys2Bench huggingface dataset:
Question: If p<0, which of the following must be true?
Options:
A)–100 < p < 100
B)p ≤ –1
C)p ≤ 1
D)p^2 ≥ 1/4
E)–100 < p < 0
Rationale: p is a negative number.
A. –100 < p < 100p can be a negative number less than -100
B. p ≤ –1p can be a fraction, in which case it would be greater than -1
C. p ≤ 1must be true since 1 is positive and p is negative
D. p^2 ≥ 1/4not true if p is a negative fraction like -1/5
E. –100 < p < 0p can be a negative number less than -100=C
Answer: C
Question: A man can row with a speed of 12 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?
Options:
A)22
B)28
C)20
D)82
E)23
Rationale: M = 12
S = 11
DS = 12 + 11 = 23. Answer:E
Answer: E
Question: What is the minimum number of square marbles required to tile a floor of length 2 metres 89 cm and width 3 metres 74 cm?
Options:
A)176
B)187
C)374
D)748
E)546
Rationale: The marbles used to tile the floor are square marbles.
Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble.
As we have to use whole number of marbles, the side of the square should a factor of both 2 m 89 cm and 3m 74. And it should be the highest factor of 2 m 89 cm and 3m 74.
2m 89 cm = 578 cm and 3 m 74 cm = 374 cm.
The HCF of 289 and 374 = 34.
Hence, the side of the square is 17.
The number of such square marbles required,
=289×374/17×17
=374 marbles
Option(C)
Answer: C
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 1
II. y = 0
III. x = 0
Options:
A)I only
B)II only
C)III only
D)I and III only
E)I, II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer C
Answer: C
Question: The sum of the numbers is 110. If the first number be twice the second and third number be one-third of the first, then the second number is:
Options:
A)30
B)54
C)72
D)84
E)27
Rationale: Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 110
11x/3 = 110
x = 30
ANSWER:A
Answer: A
Question: If the sides of a triangle are 39 cm, 32 cm and 10 cm, what is its area?
Options:
A)120
B)772
C)288
D)160
E)2848
Rationale: The triangle with sides 39 cm, 32 cm and 10 cm is right angled, where the hypotenuse is 39 cm.
Area of the triangle = 1/2 * 32 * 10 = 160 cm2
Answer: D
Answer: D
Question: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $250. Find the original price of petrol?
Options:
A)$11
B)$5
C)$45
D)$400
E)$5.5
Rationale: Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 250/45=$5.5
Answer: E.
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 21 sec. What is the length of the train?
Options:
A)350
B)150
C)277
D)258
E)191
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 21 = 350 m
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 1w widgets.
Options:
A)4
B)6
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.
Answer : B
Answer: B
Question: Mark is playing poker at a casino. Mark starts playing with 120 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark's remaining chips are $20 chips, how much money did Mark bet?
Options:
A)$1,960
B)$1,680
C)$1,540
D)$3,080
E)$2,640
Rationale: Total chips 120
20% of $100 chips = 24 chips * $100 = $2,400
80% of $20 chips = 96 chips * $20 = $1,920
If x is the number of chips bet and y is the amount of chips remaining:
x + y = 120
y = 120 - x ~ (1)
[First round bet] + [Second round bet] = $2,400 + $1,920
[0.1x * $100 + 0.9x * $20] + [0.3y * $100 + 0.7y * $20] = $4,320
10x + 18x + 30y + 14y = 4320
28x + 44y = 4320 ~ (2)
Substitute (1) into (2) to solve for x:
28x + 44(120 - x) = 4320
28x + 5280 - 44x = 4320
16x = 960
x = 60
Substituting x:
[First round bet] = [0.1x * $100 + 0.9x * $20] = 0.1(60)($100)+0.9(60)($20) = $600 + $1,080 = $1,680
Answer is B
Answer: B
Question: Walking at 75% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
Options:
A)30
B)36
C)42
D)48
E)72
Rationale: speed is inversly proprtional to time
walking at 75% of speed meand 3/4s takes 4/3t.
It takes 24 minutes extra to cover the distance. then
4/3t=t+24
4t=3t+72
t=72
Option E is correct
Answer: E
Question: Jason is 4 times older than Bob at present. 8 years ago Jason was 12 times older. How old are Bob?
Options:
A)11
B)22
C)33
D)44
E)55
Rationale: Jason age y=4(x)----(1), let us say Jason is x and bob is y
after 8 years Jason age is 8 12 time older than bob so y-8=12(x-8)---(2)
replace (2) equation y with with equation (1) value solve we get x=11 so y=44
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 50 percent of the total number of employees work in research, how many male employees do NOT work in research?
Options:
A) 520
B) 480
C) 392
D) 208
E) 188
Rationale: total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =50% =500
Total male employees =48%=480
male employees working in research =500-208=292
male employees not working in research =480-292=188
Answer E
Answer: E
Question: For what value of 'm' will the quadratic equation x2 - mx + 4 = 0 have real and equal roots?
Options:
A)16
B)8
C)2
D)-4
E)Choice (B) and (C)
Rationale: Explanatory Answer
Any quadratic equation of the form ax2 + bx + c = 0 will have real and equal roots if its discriminant b2 - 4ac = 0.
In the given equation x2 - mx + 4 = 0, a = 1, b = -m and c = 4.
Therefore, b2 - 4ac = m2 - 4(4)(1) = m2 - 16.
The roots of the given equation are real and equal.
Therefore, m2 - 16 = 0 or	m2 = 16 or m = +4 or m = -4.
Hence, answer choice (D)
Answer: D
Question: What is the place value of 6 in the numeral 6259
Options:
A)A)2700
B)B)2800
C)C)6000
D)D)2980
E)E)3000
Rationale: 6 * 1000 = 6000
C
Answer: C
Question: A jar contains 5 black and 2 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?
Options:
A)2/7
B)5/21
C)4/21
D)3/7
E)1/2
Rationale: P(1st black, 2nd white) = 5/7*2/6 = 10/42;
P(1st white, 2nd black) = 2/7*5/6 = 10/42.
P = 10/42 + 10/42 = 20/84= 10/42 = 5/21
Answer: B.
Answer: B
Question: This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 4 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 4 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?
Options:
A) 9P6
B) 9P3
C) 9C4
D) 9C6
E) 69
Rationale: since we have to select random 4 numbers from 9 and they all are distinct. i think it should be 9C4 or C
Answer: C
Question: if m>0 and y is m percent of x, then, in terms of m, x is what percent of y?
Options:
A)a)100m
B)b)1/100m
C)c)10000/m
D)d)10/m
E)e)1000/m
Rationale: Given (m*x)/100=y
to find (x/y)*100
Rearranging first equation
x/y*100 = 100*100/m
=10000/m
Answer C
Answer: C
Question: Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $35.88. How much did the meal cost without the tip?
Options:
A)$28.98
B)$29.91
C)$30.15
D)$31.20
E)$30.85
Rationale: The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $35.88:
1.15x = 35.88
Divide both sides by 1.15:=>x=35.88/1.15=31.20
correct answer D)$31.20
Answer: D
Question: A man takes
5
5 hours
45
45 min in walking to a certain place and riding back. He would have gained
2
2 hours by riding both ways. The time he would take to walk both ways is
Options:
A)7 hr 45 mins
B)12hr
C)4hr
D)8 hr 2 min
E)45 hr
Rationale: Explanation:
Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back.
Therefore,
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 mins
Hence, the time he would take to walk both ways
=5 hours 45 min + 2 hours=7 hours 45 mins
Answer A
Answer: A
Question: If the average of seven numbers is 35. If one is included. The average become 40. The included number is:
Options:
A)70
B)75
C)76
D)78
E)79
Rationale: 75
Option 'B'
Answer: B
Question: Forty ladies and fifty gentlemen are present at a party. There are 20 couples among them. If a lady and a gentleman is selected at random, what is the probability that they will be not be a couple?
Options:
A)1/200
B)1/100
C)99/100
D)1/40
E)1/20
Rationale: In how many ways we can select a woman and a man from 40 women and 50 men? In 40*50 = 2,000 ways.
We have a total of 20 couples so, the probability of selecting a couple is 20/2,000 = 1/100.
the probability that they will be not be a couple = 1 - probability of selecting a couple
= 1 - (1/100)
= 99 / 100
Ans- C
Answer: C
Question: Factory X's bulbs work for over 5000 hours in 75% of cases, whereas factory Y's bulbs work for over 5000 hours in 65% of cases. It is known that factory X supplies 70% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
Options:
A)76.4%
B)78%
C)77.4%
D)72%
E)73.9%
Rationale: For X, 70% of 75% will work.
For Y, 30% of 65% will work. *30% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.70(0.75) = .525
0.30(0.65) = 0.195
The combined probability then is 52.5 + 19.5 = 72%
ANS D
Answer: D
Question: A certain tire company can produce tires at a cost of $22,500 per batch plus $11 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire?
Options:
A)$7.50
B)$9.50
C)$11.00
D)$13.50
E)$20.00
Rationale: CP(15000 tires) = $22500 +($11×15000) =$187500
SP (15000 tires) = $20×15000 = $300000
Profit = SP-CP
= $300000-$187500= $112500
PROFIT/TIRE = $112500/15000 = $7.50
Answer A
Answer: A
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:
Options:
A)120
B)589
C)630
D)240
E)210
Rationale: Explanation:
Let C's share = Rs. x/4, A's share = Rs.(2/3 x x /4)=Rs(x/6)
x/6+x/4+x=1360
17 x/12=Rs. 960
Hence, B's share = Rs.(960/4)=Rs.240
Answer is D
Answer: D
Question: Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Friday, how many croissants will Marina eat on the 28th of that month?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: She eat as follow
Mon - 1
Tue - 2
Wed - 3
Thr - 5
Fri - 1(since she had more than 4 previous day)
sat - 6
sunday - 1 (since she had more than 4 previous day)
so 28th day of month she will have 5.
Answer is D
Answer: D
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 4 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)11
B)10
C)8
D)12
E)7
Rationale: Suppose they meet x hours after 4 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 7 a.m.
Answer: E
Answer: E
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was:
Options:
A)11 years
B)14 years
C)77 years
D)88 years
E)99 years
Rationale: Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5) = 14 years.
Answer:B
Answer: B
Question: 64, 81, 100, 144, 196, ?, F ind the missing number(?).
Options:
A)225
B)220
C)230
D)238
E)278
Rationale: The series consists of squares of consecutive composite numbers.
Answer : A.
Answer: A
Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
Options:
A)17
B)12
C)15
D)19
E)65
Rationale: Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64
= 16P => P = 19.
Answer:D
Answer: D
Question: If 2x = 3y = 10, then 15xy = ?
Options:
A) 1,200
B) 200
C) 120
D) 40
E) 250
Rationale: 2x = 10;x=5
3y = 10;y=10/3
Multiply: 15xy=15*5*10/3=250
Answer: E.
Answer: E
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
Options:
A)22
B)24
C)27
D)30
E)32
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
C
Answer: C
Question: In a ratio which is equal to 2:4, if the antecedent is 50, then the consequent is?
Options:
A)72
B)85
C)100
D)51
E)80
Rationale: We have 2/4 = 50/x
2x = 50*4
x = 100
consequent = 100
Answer is C
Answer: C
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (4,4) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Options:
A)0
B)2/5
C)4/7
D)1
E)-4
Rationale: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.
The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (7,4) OR Midpoint of (0,4) and (7,0)
i.e. Either [(0+7)/2, (0+4)/2] OR [(0+7)/2, (4+0)/2] =[3.5, 2]
Slope of line passing through points (4,4) and (3.5,2) = (4-2)/(3.5-4) = -4
E
Answer: E
Question: Beginning in Town A, Biker Bob rides his bike 8 miles west, 5 miles north, 4 miles east, and then 15 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
Options:
A)25 miles
B)20.4 miles
C)30 miles
D)32 miles
E)33 miles
Rationale: Using Pythagoras we have one side i,e total distance traveled in north direction = 15+5=20m
other being the base ie distance traveled west- distance traveled eat=8- 4= 4 m
now this third side or the distance between town A and Town B=20^2+ 4^2=sq root 416=20.4 miles
Answer : B
Answer: B
Question: A tourist purchased a total of $1,100 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
Options:
A)$1,430
B)$1,310
C)$1,290
D)$1,270
E)$870
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1100 - 230 = 870 hence answer is E
Answer: E
Question: Find the cost of fencing around a circular field of diameter 40 m at the rate of Rs.3 a meter?
Options:
A)400
B)370.4
C)376.98
D)340.9
E)350.03
Rationale: 2 * 22/7 * 20 = 125.66
125.66 * 3= Rs.376.98
Answer: C
Answer: C
Question: 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Options:
A)26
B)22
C)12
D)24
E)None of these
Rationale: Explanation :
Let the required number of days be x
More men, less days (indirect proportion)
Hence we can write as
Men36:27}::x:18
⇒36×18=27×x⇒12×18=9×x⇒12×2=x⇒x=24 . Answer : Option D
Answer: D
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 80 metres?
Options:
A)16 seconds
B)65 seconds
C)78 seconds
D)12 seconds
E)21 seconds
Rationale: Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 80/5 = 16 seconds.
Answer:A
Answer: A
Question: The average monthly salary of 660 workers in a factory is Rs. 380. The average monthly salary of officers is Rs. 2100 and the average monthly salary of the other workers is Rs. 340. Find the number of other workers.
Options:
A)645
B)650
C)640
D)642
E)none
Rationale: Solution: Total salary of 660 workers = 660*380 = Rs. 250800;
If other workers be x; then,
[(660-x)*2100]+340x = 250800
Or, 1386000-2100x+340x = 250800
1760x = 1135200
Hence, x = 1135200/1760 = 645
Number of other workers = 645.
Answer: Option A
Answer: A
Question: There are 6 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
Options:
A)90
B)120
C)225
D)180
E)200
Rationale: Number of ways of selecting 2 fiction books = 6C2
Number of ways of selecting 2 non fiction books = 6C2
6C2 * 6C2 = 15 * 15 = 225
Answer: C
Answer: C
Question: mixture contains alcohol and water in the ratio 4 : 3. If 4 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
Options:
A)20
B)99
C)27
D)22
E)29
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
16x = 4(3x+5)
4x = 20
x = 5
Quantity of alcohol = (4 x 5) litres = 20 litres.
Answer: A
Answer: A
Question: If the value of a piece of office decreases by 10% while the new tax rate on the office represent 110% of the original tax rate, what is the effect on the taxes?
Options:
A)a - taxes increase by 10%
B)b- taxes increase by 1%
C)c- there is no change in taxes
D)d- taxes decrease by 1%
E)c- taxes decrease by 10%
Rationale: Cansider the value of office = 100, Original tax rate 10%, hence tax value = 100*10% = 10.
Decreased value of office = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9
10-9.9 = decrease by 1%.
Answer D.
Answer: D
Question: A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 16,200, then what is B's share in the profit?
Options:
A)Rs. 2000
B)Rs. 3000
C)Rs. 4000
D)Rs. 5000
E)None of these
Rationale: Explanation :
Ratio of the initial investment = 7/2 : 4/3 : 6/5
= 105 : 40 : 36
From this ratio, we can assume that actual initial investments of A, B and C
are 105x, 40x and 36x respectively
A increases his share 50% after 4 months. Hence the ratio of their investments =
(105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12
= 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3
= 105 * 4 : 40 *3 : 36 * 3
= 35 * 4 : 40 : 36
= 35 : 10 : 9
B's share = total profit * (10/54) = 16,200 * 10/54 = 3000. Answer : Option B
Answer: B
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1:96
B)1:29
C)2:29
D)1:38
E)1:97
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x
= 1:96.
Answer: A
Answer: A
Question: Connie has a number of gold bars, all of different weights. She gives the 24 lightest bars, which weigh 45% of the total weight, to Brennan. She gives the 13 heaviest bars, which weigh 26% of the total weight, to Maya. She gives the rest of the bars to Blair. How many bars did Blair receive?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: Solution: The average weight of the bars given to Brennan (light) < the average weight of the bars given to Blair < the average weight of the bars given to Maya (heavy).
Let the total weight of all the bars be X.
The weight of the bars given to Brennan,
= 45% of X = 0.45X
The weight of the bars given to Maya,
= 26 % of X = 0.26X
The weight of the bars given to Claire = rest = 29% of X = 0.29X
The average weight of the bars given to Brennan,
= Weight / number of bars = 0.45X/24
The average weight of the bars given to Maya = Weight / number of bars = 0.26X/13
Similarly, if the number of bars given to Blair = B,
then the average weight of the bars given to Blair = 0.29X/B
As, the average weight of the bars given to Brennan (light) < the average weight of the bars given to Blair < the average weight of the bars given to Maya
Answer: Option B
Answer: B
Question: If thrice the age of the son is added to the father then the sum would be 56. But if twice the age of father is added to the son then the total would be 72. Find the ages of father and son.
Options:
A)32, 8
B)8, 32
C)56, 72
D)72, 56
E)32, 4
Rationale: Let the age of the father be x and the age of the son be y
x+3y=56---Eq1
2x+y=72--Eq2
multiplying Eq1 by 2 and solving the above equations we get y=8
Substitute y=8 in 2 we get x=32
answer is 32, 8 correct ans is A
Answer: A
Question: A box contains 8 red marbles, 6 green marbles & 10 pink marbles. One marble is drawn at random from box. What is the probability that the marble drawn is green?
Options:
A)6/4
B)8/4
C)10/4
D)7/4
E)1/4
Rationale: 6c1/24c1=6/24=1/4
ANSWER:E
Answer: E
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
Options:
A)10 years
B)77 years
C)88 years
D)44 years
E)33 years
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer:A
Answer: A
Question: If x > 0, which of the following could be true?
I. x^3 > x^2
II. x^2 = x
III. x^2 > x^3
Options:
A)I only
B)I & II
C)II & III
D)All of the above
E)None of the above
Rationale: I. x^3>x^2
For x = 2,
2^3>2^2
II. x^2=x
For x = 1,
1^2=1
III. x^2>x^3
For x=1/2,
(1/2)^2>(1/2)^3
All conditions could satisfy
Answer = D
Answer: D
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)6
C)7
D)54
E)3
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5.Answer:A
Answer: A
Question: Company A has an annual budget for a certain project, and 1/4 of this budget was spent during the first quarter of the year. If 1/8 of the remainder of the budget was spent during the second quarter, what fraction of the budget was left at the end of the second quarter?
Options:
A)5/8
B)13/16
C)21/32
D)37/48
E)53/64
Rationale: Let x be the company budget.
At the end of the first quarter, the remaining budget was (3/4)x.
At the end of the second quarter, the remaining budget was (7/8)(3/4)x = (21/32)x.
The answer is C.
Answer: C