divelab/Sys2Bench huggingface dataset:
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 612 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
Options:
A)170
B)179
C)196
D)240
E)200
Rationale: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(612-9-90*2)/3=240
Answer : D
Answer: D
Question: Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 85. If Jerry wants to raise his average by 3 points, what score must he earn on the fourth test?
Options:
A)97
B)89
C)90
D)93
E)95
Rationale: Total score on 3 tests = 85*3 = 255
Jerry wants the average to be = 88
Hence total score on 4 tests should be = 88*4 = 352
Score required on the fourth test = 352 - 255 = 97
Option A
Answer: A
Question: Sum of ages of two friends is 32 while difference is 2 then their ages are
Options:
A)15 years, 17 years
B)17 years, 15 years
C)16 years, 18 years
D)18 years, 16 years
E)None
Rationale: 17,15
ANSWER:B
Answer: B
Question: There are three foam generators in the factory, each of the first two can generate 14 liters of foam in one hour and the third can generate 20 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
Options:
A)120.
B)132.
C)146.
D)161.
E)166.
Rationale: Let the foam generators capacity be -
A = 14 lit/hr
B = 14 lit/hr
C = 20 lit/hr
Total foam generation in 1 hour will be 48 lit ( 14 + 14 + 20 ) ; since in 1 and 1/2 hr they will generate 48 + 24 => 72 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 14 lit/hr
C = 20 lit/hr
Total foam generation in 2 hour will be 68 litres {2 (14+20)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 14 => 21 litres
So, total foam generated will be 161 Litres ( 72 + 68 + 21 ) ; hence answer will be (D)
Answer: D
Question: For how many integers n is 1^n+4 = (n+4)^1?
Options:
A)1
B)2
C)3
D)None of these
E)4
Rationale: If n=0
1^0+4= (0+4)^1
1^4 = 1 ; 4^1 =4 not ok
If n=1
1^1+4 =1 ; (1+4)^1=5^1=5 not OK
So, Answer : D
Answer: D
Question: An investment of d dollars at k percent simple annual interest yields $400 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $1,600 over a 5 year period?
Options:
A)(2d)/3
B)(3d)/4
C)(4d)/3
D)(3d)/2
E)(8d)/5
Rationale: 400 dollars in 2 years means 200 dollars in 1 year.
To get 1600 dollars' it will take 8 years.
To get 1600 in 5 years, we need 8/5 times money. Answer is E.
Answer: E
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
Options:
A)10 hours
B)17 hours
C)12 hours
D)50 hours
E)16 hours
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer:A
Answer: A
Question: The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2?
Options:
A)2 + s + a
B)22 + a
C)2s
D)2a + 2
E)4 + a
Rationale: Here for The series
s,s+1...s+4 => mean = median = s+2 =a
hence for the next 9 consecutives => a,a+1,a+2...
=> Mean = Median = a+a+8/2 = a+4
ANSWER:E
Answer: E
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
Options:
A)337
B)299
C)277
D)646
E)271
Rationale: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Answer: D
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 45%. Staff are allowed a further 40% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
Options:
A)0.35D
B)0.76D
C)0.65D
D)0.77D
E)0.33D
Rationale: Effective discount = a + b + ab/100 = - 45 - 40 + (-45)(-40)/100 = -67
Sale price = D * ( 1 - 67/100)
Sale price = .33 * D
Answer (E)
Answer: E
Question: June 25, 1982, fell on a Friday. On which day of the week did December 25, 1983, fall?
Options:
A) Sunday
B) Monday
C) Tuesday
D) Wednesday
E) Thursday
Rationale: 6/25/82 - 12/25/83
The date range contains one full year of 365 days plus a partial year. The number of days in the partial year is:
June - 5, July - 31, August - 31, September - 30, October - 31, November - 30, and December - 25.
5 + 31 + 31 + 30 + 31 + 30 + 25 = 183.
183 + 365 = 548 total days in the date range.
Divide by 7 to determine how much the day of the week advances: 548 / 7 = 78 remainder 2.
Since the first date was a Friday, advance the day of the week by 2; the second date fell on a Sunday. The answer is A.
Answer: A
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)167m
B)180m
C)187m
D)287m
E)276m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: B
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
Options:
A)387 m
B)287 m
C)175 m
D)187 m
E)167 m
Rationale: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer: C
Answer: C
Question: One fourth of a solution that was 10 percent gram flour by weight was replaced by a second solution resulting in a solution that was 16 percent gram flour by weight. The second solution was what percent gram flour by weight ?
Options:
A)34%
B)24%
C)22%
D)18%
E)8.5%
Rationale: EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of gram flour in 2nd sol)=34%=A
Answer: A
Question: How many numbers between 101 and 250, exclusive are divisible by three?
Options:
A)34
B)41
C)50
D)83
E)148
Rationale: Numbers upto 250 divisible by 3 is 250/3 = 83
Numbers upto 101 divisible by 3 is 101/3 = 33
Total number of numbers between 101 and 250 that are divisible by 3 is 83 - 33 = 50
ANSWER:C
Answer: C
Question: In a poll of 44,000 dentists, only 30 percent responded; of these, 20 percent claimed to prefer Toothpaste A. How many of the dentists who responded did not claim a preference for Toothpaste A?
Options:
A)2,200
B)2,640
C)6,160
D)8,800
E)10,560
Rationale: Find those who responded to the poll-
44000∗3/10=4400∗3=13200
Find those who responded who do not prefer toothpaste A-
13200∗8/10=1320∗8=10560
ANSWER:E
Answer: E
Question: Solve:-
111 x 111 x 111 + 555 x 555 x 555 = ?(111 x 111 - 111 x 555 + 555 x 555)
Options:
A)888
B)666
C)555
D)988
E)889
Rationale: Given Exp. = (a3 + b3) = (a + b) = (111 + 555) = 666 (a2 - ab + b2)
Answer B
Answer: B
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 28 have long fur, 17 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
Options:
A)26
B)19
C)11
D)8
E)6
Rationale: No of dogs=45
Long fur=28
Brown=17
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=28+17-Both
Both=8
Answer D
Answer: D
Question: If K is the sum of reciprocals of the consecutive integers from 3 to 8, inclusive, then K is closest in value to which of the following?
Options:
A)1.2
B)1/10
C)1/8
D)1/6
E)1/4
Rationale: 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8
=0.33+0.25+0.20+0.16+ 0.14+0.12=1.2
A
Answer: A
Question: A student got twice as many sums wrong as he got right. If he attempted 36 sums in all, how many did he solve correctly ?
Options:
A)12
B)16
C)18
D)24
E)26
Rationale: Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 36 3x = 36 x = 12.
Answer:A
Answer: A
Question: A gang of 8 boys goes on an tour in 2cars, of which 1can seat 5 & the other only 4. In how many ways can they travel?
Options:
A)100
B)121
C)126
D)128
E)130
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Answer: C
Question: If P is a prime number greater than 3, find the remainder when p^2 + 17 is divided by 12.
Options:
A)6
B)1
C)0
D)8
E)7
Rationale: Take any prime number greater than 3 and check -
Say p = 5
So, p^2 + 17 = 25+17 => 42
42/12 will have remainder as 6
Say p = 7
So, p^2 + 17 = 49+17 => 66
66/12 will have remainder as 6
So answer will be (A) 6
Answer: A
Question: If the numerator of a fraction be increased by 12% and its denominator decreased by 2% the value of the fraction becomes 6/7. Thus, the original fraction is:
Options:
A)1/4
B)2/4
C)3/4
D)2/3
E)1/3
Rationale: If original fraction is x/y , then
1.12x/0.98y = 6/7
(8/7)*(x/y)=6/7
x/y =6/8=3/4
ANSWER:C
Answer: C
Question: In a 100 m race, A runs at 8km per hour. If A gives B a start of 9 m and still him by 15 seconds, what is the speed of B ?
Options:
A)5.46 km/hr.
B)5.56 km/hr.
C)5.76 km/hr.
D)6.76 km/hr.
E)5.72 km/hr.
Rationale: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.
B covers (100 - 9) m = 91 m in (45 + 15) sec = 60 sec.
B's speed = (91 x 60 x 60)/(60 x 1000)km/hr = 5.46 km/hr.
Answer is A
Answer: A
Question: Difference between two numbers is 5, six times of the smaller lacks by 4 from the four times of the greater. Find the numbers?
Options:
A)5,3
B)7,5
C)9,7
D)11,9
E)13,8
Rationale: Explanation:
x – y = 5
4x – 6y = 4
x = 13 y = 8
E)
Answer: E
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets T did Irwin score?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored T=2 11-point baskets in my opinion.
Answer C
Answer: C
Question: X can do a piece of work in 8hours. Y and Z together can do it in 6 hours, while X and Z together can do it in 4 hours. How long will Y alone take to do it?
Options:
A)24 HOURS
B)20 HOURS
C)34 HOURS
D)12 HOURS
E)10 HOURS
Rationale: X's 1 hour work= 1/8
(Y+Z)'s 1 hour work= 1/6
(X+Z)'s 1 hour work= 1/4
(X+Y+Z)'s 1 hour work= (1/8+1/6)=7/24
Y's 1hour's work= (7/24-1/4)= 1/24
Y alone will take 24 hours to do the work.
correct option is A
Answer: A
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
Options:
A)250
B)203
C)200
D)195
E)None of these
Rationale: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER: D
Answer: D
Question: A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed
against the current will be
Options:
A)11 kmph
B)10 kmph
C)14 kmph
D)17 kmph
E)None of these
Rationale: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 5 = 15
Now speed against the current will be
speed of the man - speed of the current
= 15 - 5 = 10 kmph
Answer: B
Answer: B
Question: Three pipes A, B and C can fill a tank from empty to full in 20 minutes, 20 minutes and 30 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution Q in the liquid in the tank after 3 minutes?
Options:
A)5/8
B)6/8
C)4/8
D)2/8
E)3/8
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/20 + 1/20 + 1/30) = 6/15
Part filled by B in 3 minutes = 3/20
Required ratio = 3/20 * 15/6 =3/8
Answer:E
Answer: E
Question: Two trains 180 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9
B)10.7
C)10.3
D)10.8
E)12.24
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 180 + 160 = 340 m.
Required time = 340 * 9/250 = 306/25 = 12.24sec.
'Answer: E
Answer: E
Question: Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is:
Options:
A)24
B)54
C)34
D)45
E)25
Rationale: D = 10x + y
S = 10x^2 + y^2
S-D --> (10x^2 + y^2) - (10x + y) = 27 --> 10x (x-1) + y (y+1) = 27
ANSWER:B
Answer: B
Question: If 17m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
A)2m −1
B)4m
C)6m
D)m/5
E)6m/5
Rationale: 17m - n = p
Add n to both sides:
17m = n + p
Add m to both sides:
18m = n + p + m
Now, divide both sides by 3
6m = (n + p + m)/3 = the average of n, p, and m
C
Answer: C
Question: When positive integer n is divided by 4, the remainder is 1. When n is divided by 7, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 35?
Options:
A)1
B)2
C)5
D)19
E)20
Rationale: When positive integer n is divided by 4, the remainder is 1 i.e., n=4x+1
values of n can be one of {1, 5, 9, 13, 17, ...........29, 33, 37..................}
Similarly,
When n is divided by 7, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 12, 19, 26, 33, 40,........}
combining both the sets we get
n={5,33, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 35 or 35x
in case of n=33 p=2
so for min value of p, we take min value of n.
B is the answer.
Answer: B
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
Options:
A)277 m
B)704 m
C)278 m
D)288 m
E)378V
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: The average age of husband, wife and their child 3 years ago was 24 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A)31 years
B)40 years
C)50 years
D)55 years
E)None
Rationale: Solution
Sum of the present ages of husband, wife and child	= (24x3+3x3) years
= 81 years.
Sum of the present ages of wife and child	= (20x2+5x2) years
= 50 years.
âˆ´ Husband's present age	= (81 - 50) years
= 31 years.
Answer A
Answer: A
Question: In a store there is a number of people, out of which 1/30 are children, 1/6 are women and the remaining 120 are men. How many children are in the store?
Options:
A)50
B)120
C)150
D)5
E)25
Rationale: Let x be the number of people in the store.
x/30+x/6=6x/30=x/5 is the number of children and women
The number of men is x-x/5=4x/5, that is 4x/5=120. Thus, x=150.
The number of children is 1/30*150=5.
Answer D 5.
Answer: D
Question: An article is bought for Rs.1450 and sold for Rs.1420, find the loss percent?
Options:
A)2%
B)4%
C)6%
D)8%
E)12%
Rationale: 1450 ---- 30
100 ---- ? => 2%
Answer:A
Answer: A
Question: If the LCM of 9, 7, 2, and q is 504, which of the following could be q?
Options:
A)7
B)8
C)6
D)9
E)5
Rationale: Using elimination method, eliminate the option to arrive at 8
if x is replaced by 8 and the LCM is calculated you arrive at 504
B
Answer: B
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.27000. A's share is?
Options:
A)s.7500
B)s.7200
C)s.6000
D)s.5750
E)s.9000
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 27000 = 9000
ANSWER:E
Answer: E
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. x+ y > z
III. yz > xz
IV. xy > y + z
Options:
A)I only
B)II only
C)II and III only
D)II and IV only
E)III and IV only
Rationale: lets see the choices..
I. x > z...
we do not know the values or the relative values ... need not be true..
II. x+ y > z
we take the worst case that z is the largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y.. need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ANSWER:B
Answer: B
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y − 2)
II. z<(x − 1)/(y − 2)
III. z>(x + 1)/(y + 2)
Options:
A)I only
B)I and II
C)II and III
D)II only
E)I and III
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y − 2) --> 2/3 > 1/1 --> False
II. z<(x − 1)/(y − 2) --> 2/3 < 1/1 --> True
III. z>(x + 1)/(y + 2) --> 2/3 > 3/5 --> True
Answer: C
Answer: C
Question: 24 oz of juice P and 25 oz of juice T are mixed to make smothies X and Y . The ratio of p to T in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to T ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice T will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice T = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Answer: D
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 120 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 6 o'clock?
Options:
A)60 miles
B)80 miles
C)110 miles
D)120 miles
E)400 miles
Rationale: Answer = C. 110 miles
Relational speed = 120 - 100 = 20 miles per hour
In 4 hours, difference = 20 * 4 = 120 miles
Fast train trailing 10 miles, so effective difference = 120 - 10 = 110 miles
Answer: C
Question: Jack took a 3-hour bike ride. In the second hour he travlled 18 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
Options:
A)54.0
B)54.9
C)55.5
D)57.0
E)63.0
Rationale: Let the distance travelled in the first hour be x. Thus, 1.2x = 18 , x = 15. Now, the distance travelled in the 3rd hour = 18+1/4∗18 = The only option ending with a 0.5 in the decimal's place is C.
Correct answer is C
Answer: C
Question: The bankers discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
Options:
A)Rs. 360
B)Rs. 432
C)Rs. 540
D)Rs. 1080
E)Rs. 1280
Rationale: Sum = (B.D*T.D)/(B.D-T.D)
(72*60)/72-60;
360
ANSWER:A
Answer: A
Question: The train leaves from New York City every 40 minutes from Boardman station. A man told John Watson that the train had left 15 minutes ago and the next train to New York City will leave at 9:40 p.m. At what time, man convey this information to John Watson?
Options:
A)6:15 PM
B)7:15 PM
C)8:15 PM
D)9:15 PM
E)None
Rationale: Solution
Time of John Watson last missed the train = 8:40 PM - 40 min = 8:00 PM As this information has been given to John Watson 15 minutes after the train has already left, the man gave the information at 8:00 p.m. + 15 min = 8:15 PM
Answer C
Answer: C
Question: In order to obtain an income of Rs. 15000 from 80% stock at Rs. 200, one must make an investment of
Options:
A)Rs.30000
B)Rs.37000
C)Rs.37500
D)Rs.40000
E)Rs.40500
Rationale: Explanation :
Market Value = Rs. 200.
Required Income = Rs. 15000.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.80 (ie,80% of the face value 100), investment = Rs.200
To obtain Rs.15000, investment = 200/80Ã—15000=Rs.37500
Answer : Option C
Answer: C
Question: emblem is coded as 216;
crude is coded as 125
hi will be ?
Options:
A)243
B)64
C)8
D)32
E)16
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
hi = 2^3 =8
ANSWER:C
Answer: C
Question: A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain?
Options:
A)12.5%
B)16.7%
C)22.5%
D)27.5%
E)33.3%
Rationale: Let x be the original number of each color so there are a total of 5x candies.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.2x
red + yellow = 0.45x
red = 0.225x, since red = yellow.
The answer is C.
Answer: C
Question: Three pieces of timber 48 m, 56 m and 72 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
Options:
A)8 m
B)4 m
C)2 m
D)6 m
E)None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 48, 56, 72 = 8 m
Correct Option: A
Answer: A
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
Options:
A)2/113
B)3/115
C)1/108
D)2/213
E)3/215
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: C
Question: The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 21. What is the last numbers?
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: A + B + C = 18
B + C + D = 15
A + D = 21
A – D = 3
A + D = 21
2D = 18
D = 9
ANSWER:E
Answer: E