divelab/Sys2Bench huggingface dataset:
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 6 units?
Options:
A)140
B)84
C)88
D)72
E)12
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 6 units
Area of the rectangle = lb = 14 * 6 = 84 sq.units
Answer: B
Answer: B
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that a beginner Trigonometry student is selected?
Options:
A)40%
B)44%
C)48%
D)52%
E)56%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.7x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.7x = 1.3x
The percentage in beginner trigonometry is 1.3x / 2.5x = 52%
The answer is D.
Answer: D
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 11 years, son's age will be:
Options:
A)12 years
B)14 years
C)18 years
D)20 years
E)25 years
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 11 years = (x+ 11) = 25 years..
Answer: E
Answer: E
Question: In how many ways 5 Indians and 2 Englishmen can be seated in a row so that they are alternate?
Options:
A)240
B)96
C)144
D)202
E)256
Rationale: number of ways = 5!*2! = 240
Answer is A
Answer: A
Question: f a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Options:
A)5 km
B)50 km
C)10 km
D)25 km
E)30 km
Rationale: Explanation:
Let the actual distance travelled be x km.
Then, x/10=x+20/14
14x = 10x + 200
4x = 200
x = 50 km.
ANSWER:B
Answer: B
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 50 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)10 days
C)12 days
D)50/6 days
E)16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 Ã— 50/60 = 50/6 days
D)
Answer: D
Question: 9 partners bought a restaurant for 1 million dollars. If they want to pay the same amount and none of them have bills smaller than $1, how much money would they have to pay?
Options:
A)$2,000,001
B)$2,000,003
C)$2,000,005
D)$2,000,006
E)$2,000,008
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 1,000,000 = 1 and 9 is divisible by 9.
Hence, we need to add 8 to this number for it to be divisible by 9
Correct Option: E
Answer: E
Question: If x is less than y by 40% then y exceed x by:
Options:
A)33.33%
B)25%
C)75%
D)66.66%
E)None of these
Rationale: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 40%)
=> 40/(100-40)*100
=66.66%
ANSWER:D
Answer: D
Question: A triangle has sides 10, 17, and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle. What is the length of the side of the square?
Options:
A)148/29
B)168/29
C)168/26
D)158/29
E)198/29
Rationale: By Heron's Formula, the area, A, of a triangle with sides a, b, c is given by A = square root[s(s − a)(s − b)(s − c)], where s = ½(a + b + c) is the semi-perimeter of the triangle.
Then s = ½(10 + 17 + 21) = 24, and A = 84.
A square inscribed in a 10 by 17 by 21 triangle, with perpendicular dropped onto the side of length 21.
Now drop a perpendicular of length h onto the side of length 21.
We also have A = ½ × base × perpendicular height.
Hence A = 21h/2 = 84, from which h = 8.
Notice that the triangle above the square is similar to the whole triangle. (This follows because its base, the top of the square, is parallel to the base of the whole triangle.)
Let the square have side of length d.
Considering the ratio of altitude to base in each triangle, we have 8/21 = (8 − d)/d = 8/d − 1.
Therefore the length of the side of the square is 168/29.
ANSWER:B
Answer: B
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)66
B)11
C)40
D)21
E)23
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) = 40 seconds.Answer: C
Answer: C
Question: When E is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when E + y is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: In my view the answer should be C
E/5 has Remainder=3 -> E = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Answer: C
Question: David spends $350 buying his favorite dolls. If he buys only small LemonHead dolls, which are $2 cheaper than the large LemonHead dolls, he could buy 20 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?
Options:
A)$5
B)$7
C)$6
D)$8
E)$9
Rationale: If large doll costs $5, then he can buy 350/5 = 70 large dolls and 350/3 =116 small dolls. Difference is more than 20. Discard.
If large doll costs $7, then he can buy 350/7 = 50 large dolls and 350/5 =70 small dolls.
Difference is 20, which is we wanted.
Answer B.
Answer: B
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability Z that all three secretary are assigned at least one report?
Options:
A)8/9
B)64/81
C)4/9
D)16/81
E)5/9
Rationale: For each report there are three possible outcomes: Secretary A, Secretary B, Secretary C
Total outcome: 3^3=27
Total outcome that three secretary are assigned at least one report: P(3,3)=3!=6
Probability Z= 6/27=2/9=C
Answer: C
Question: A certain hospital has a policy that for every 50 patients there should be 2 doctors. If the number of patients visiting the hospital every day is 400, how many doctors are there in the hospital?
Options:
A)4
B)16
C)5
D)14
E)11
Rationale: 2/50=x/400
x=16
Answer is B
Answer: B
Question: There are two cars. One is 160 miles north of the other. Simultaneously, the car to the north is driven westward at 10 miles per hour and the other car is driven eastward at 30 miles per hour. How many miles apart are the cars after 3 hours?
Options:
A)180
B)200
C)220
D)240
E)250
Rationale: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 120 and a height of 160. The hidden pattern here is a 3/4/5 right triangle (the 120 lines up with the '3' and the 160 lines up with the '4'). In this way, you can deduce that each side is '40 times' bigger than it's corresponding side:
3/4/5 becomes
120/160/200
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer:
B
Answer: B
Question: In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)45%
C)32%
D)40%
E)28%
Rationale: answer b
male-employed - 64%
female-employed-19%
Total employed 64%
means total unemployed = 36%
therefore d and e are not correct because female unemployed has to be less than 36%
female-unemployed = 32% male unemployed = 4%
48% + 4% = 52%
16% + 32% = 48%
plug in a and b in place of 32% and the sum is not 100%
19/64 =28 E
Answer: E
Question: Tom can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4shots. What is the probability that at least 2 shots hit the target ?
Options:
A)1/2
B)2/5
C)2/3
D)3/7
E)3/11
Rationale: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: C
Question: A car manufacturer produces only red and blue models which come out of the final testing area at random. What is the probability that five consecutive cars of same color will come through the test area at any one time?
Options:
A)1 in 16
B)1 in 125
C)1 in 32
D)1 in 25
E)1 in 15
Rationale: 2*(1/2)^5 =1 in 16
AS THERE ARE 5 CARS AND 2 TYPES
ANSWER: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)1/21
B)1/31
C)1/108
D)1/113
E)2/213
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: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
Options:
A)50
B)55
C)100
D)25
E)52
Rationale: Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
=10 x5/18	m/sec
=25/9m/sec
2 x/36=25/9
2x = 100
x = 50.
Answer A
Answer: A
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
Options:
A)Rs.16,537.58
B)Rs.16,537.52
C)Rs.16,537.50
D)Rs.16,537.22
E)Rs.16,537.21
Rationale: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20)
= Rs. 16537.50
Answer:C
Answer: C
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.50 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options:
A)160
B)170
C)190
D)200
E)210
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.50 + X x 3.20 = 432
X = 10.
Hence, total hours of work = (160 + 10) = 170.
answer :B
Answer: B
Question: Diana is going on a school trip along with her two brothers, Bruce and Clerk. The students are to be randomly assigned into 3 groups, with each group leaving at a different time. What is the probability that DIana leaves at the same time as AT LEAST on her bothers?
Options:
A)1/27
B)4/27
C)5/27
D)4/9
E)5/9
Rationale: 3 This post received
KUDOS 1 This post was
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For "atleast" problems, its easier to do (1 - opposite of what is being asked). Here 1 - different groups
# of ways in which Diana can be assigned a group = 3
# of ways in which Bruce can be assigned a group = 2 (since bruce cannot be assigned the same group as diana)
# of ways in which Clerk can be assigned a group = 2 (since clerk cannot be assigned the same group as diana)
=> 1 - (3/3)(2/3)(2/3)
=> 5/9
ANSWER:E
Answer: E
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 13,000?
Options:
A)1,950,000,000
B)750,000
C)850,000
D)7,500,000
E)750,000,000
Rationale: number of cars sold = x=800000-50y
y=13000
x=800000-650000=150000
revenue from 150000 cars=13000*150000=1,950000000 A
Answer: A
Question: An auto supply store sells steering wheel covers arranged on display such that each of two different colors of steering wheel covers, blue, and purple are consecutive in a repeating pattern. If three consecutively displayed steering wheel covers are purchased, what is the probability that two of the steering wheel covers are purple?
Options:
A)3/4
B)2/5
C)1/4
D)2/3
E)1/2
Rationale: After blue and purple, the next steering wheel cover can be of any given two colours, therefore we have total two possibilites, out of which we need purple i.e. 1 therefore prob is 1/2. Correct answer is E.
Answer: E
Question: There are between 300 and 310 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
Options:
A) 301
B) 303
C) 306
D) 307
E) 309
Rationale: Let number of cards = x
If the cards are counted 3 at a time , there are 2 left over-
x= 3p+2
x can take values 306 , 309
If the cards are counted 4 at a time , there is 1 left over
x= 4q+1
x can take values 301 , 309
Therefore , x = 309
Answer E
Answer: E
Question: A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 16%?
Options:
A)17 per kg
B)17.40 per kg
C)16.5 per kg
D)16 per kg
E)None of these
Rationale: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 116% of 3000 = (116⁄100 × 3000) = 3480
∴ Rate of S.P. of the mixture = (3480⁄200) per kg
= 17.40 per kg.
Answer B
Answer: B
Question: When q is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when q + y is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: In my view the answer should be C
q/5 has Remainder=3 -> q = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Answer: C
Question: Find the cost of fencing around a circular field of diameter 35 m at the rate of Rs.1.50 a meter?
Options:
A)287
B)132
C)156
D)115.5
E)267
Rationale: 2 * 22/7 * 17.5 = 110
110 * 1 1/2 = Rs.115.5
Answer: D
Answer: D
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 24. What is the total number of students in the school?
Options:
A)50
B)80
C)120
D)150
E)100
Rationale: Explanation: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 24 + 2/3 of 24
80/100x = 40
x = 50.
Answer: Option A
Answer: A
Question: .A man has Rs. 312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)36
B)24
C)28
D)32
E)30
Rationale: Let number of notes of each denomination =x Then
x+5x+20x=312
⇒26x=312
⇒x=312/26=12
Total number of notes =3x=3×12=36
Answer: A
Answer: A
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 20 years now, the son's age five years back was:
Options:
A)2 years
B)14 years
C)5 years
D)38 years
E)7 years
Rationale: Let the son's present age be x years.
Then, (20 - x) = x
2x = 20 => x = 10
Son's age 5 years back = (10 - 5) = 5 years.
ANSWER:C
Answer: C
Question: A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.
Options:
A)21:25
B)27:25
C)21:23
D)31:25
E)33:22
Rationale: Solution :
Given SI1 = SI 2
P1 : P2 = 1/R1T1 : 1/R2T2
= 1/(10*5) : 1/(9:6)
27:25
B
Answer: B
Question: When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
Options:
A)339
B)349
C)369
D)359
E)Data inadequate
Rationale: Explanation:
x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
q =	2 + 13p
17
The least value of p for which q =	2 + 13p	is a whole number is p = 26
17
x = (13 x 26 + 11)
= (338 + 11)
= 349
Answer: B
Answer: B
Question: On a wedding catering service, An experienced chef can prepare a service for a wedding in 5 hours while an novice chef would finish the preparations in 9 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: Experienced chefs work = 1 wedding/5 hours
Novice chefs work = 1 wedding/9 hours
Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equalx
1hr and 36mins = 8/5 an hour
x/5 + x/9 = 1 wedding / (8/5)
x/5 + x/9 = 5/8
x=2
So there are 2 novice chefs and 2 experienced chefs. In total there are 4. The answer is C.
Answer: C
Question: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 5200 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?
Options:
A)2160
B)2350
C)2000
D)2300
E)None of these
Rationale: Explanation :
Total Exp = 5000+1500+4500+2500+2000+5200 = 20700
Exp in % = 100-10 = 90%, 20700 = 90%
Saving = 10 % = 20700 X 10/90 = Rs. 2300
Answer : D
Answer: D
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options:
A)12.8
B)12.1
C)12.0
D)12.2
E)12.4
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Answer: B
Question: A lady bought five books namely A,B,C,D,E to distribute her 7 friends. How many ways she can distribute books?
Options:
A)7^3
B)7^4
C)7^5
D)7^6
E)7^2
Rationale: 7*7*7*7*7
7^5
ANSWER:C
Answer: C
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
Options:
A)1:1
B)2:3
C)3:2
D)9:4
E)45:8
Rationale: Water:soap = 3:2
Soap:Salt=15:2
=> For 15 soap, salt = 2
=> For 2 Soap, salt = (2/15)*2 =4/15
So, water:soap:salt = 3:2:4/15 = 45:30:4
After open container, water:soap:salt = 22.5:30:4
So, water:salt = 22.5:4 = 45:8
E
Answer: E
Question: What is the ratio between perimeters of two squares one having 4 times the diagonal then the other?
Options:
A)3: 8
B)3: 6
C)3: 7
D)4: 1
E)3: 3
Rationale: d = 4d d = d
a√2 = 4d a√2 = d
a = 4d/√2 a = d/√2 => 4: 1
Answer:D
Answer: D
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 41 degrees. Find the temperature on Friday?
Options:
A)65 degrees
B)73 degrees
C)37 degrees
D)34 degrees
E)33 degrees
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 41
Tu + W + Th = 192 -41= 151
F = 184 – 151 = 33
Answer:E
Answer: E
Question: In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?
Options:
A)None of these
B)720
C)60
D)120
E)None of these
Rationale: Explanation :
1st man can draw water from any of the 5 taps
2nd man can draw water from any of the remaining 4 taps
3rd man can draw water from any of the remaining 3 taps
4th man can draw water from any of the remaining 2 taps
5th man can draw water from remaining 1 tap
5	4	3	2	1
Hence total number of ways = 5 x 4 x 3 x 2 x 1 = 120. Answer : Option D
Answer: D
Question: Which number is the odd one out?
Options:
A)47632
B)36119
C)84129
D)67626
E)72927
Rationale: A
47632
All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.
Answer: A
Question: Find the area of trapezium whose parallel sides are 10 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)287 cm2
B)785 cm2
C)285 cm2
D)785 cm2
E)210 cm2
Rationale: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (10 + 18) * (15) = 210 cm2
Answer: Option E
Answer: E
Question: The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
Options:
A)23:33:60
B)10:11:20
C)3:4:5
D)10:20:11
E)23:30:65
Rationale: Let A = 2k, B = 3k and C = 5k.
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
[A].	3 : 3 : 10
[B].	10 : 11 : 20
[C].
23 : 33 : 60	@
[D].	Cannot be determined
Answer: Option C
Explanation:
Let A = 2k, B = 3k and C = 5k.
A sal = 115/100 of 2k = 23k/10
B sal = 110/100 of 3 k=33k/10
c sal= 6k
new ratio (23k/10:33k/10:6k) = 23:33:60
ANSWER A
Answer: A
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Options:
A)5/5
B)5/9
C)3/4
D)5/7
E)5/2
Rationale: In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E	= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27
The probability = 27/36 = 3/4.
Answer: C
Answer: C
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 602 to 700 inclusive?
Options:
A)24,550
B)28,550
C)32,550
D)36,550
E)40,550
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
602 + 604 + ... + 700 = 50(600) + (2+4+...+100) = 30,000 + 2550 = 32,550
The answer is C.
Answer: C
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor G of 2x and 3y?
Options:
A)G=1
B)G=Cannot be determined
C)G=2
D)5
E)6
Rationale: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD (1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Answer: B
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam.
Options:
A)15
B)45
C)35
D)25
E)55
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 95(x - 5)
80x - (5 * 20) = 95(x - 5)
375 = 15x => x = 25
ANSWER:D
Answer: D
Question: How many of the positive factors of 10 , 16 and how many common factors are there in numbers?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: factors of 12 - 1, 2, 3, 4, 6, and 12
factors of 16 - 1 , 2, 4, 8 and 16
Comparing both, we have three common factors of 45,16-3
Answer C
Answer: C
Question: Which among the following is the greatest?
Options:
A)2^3^2
B)2^2^3
C)3^2^3
D)3^3^3
E)5^3^3
Rationale: 2^3^2 = 29
2^2^3 = 28
3^2^3 = 38
3^3^3 = 327
As 327 > 38, 29 > 28 and 327 > 29. Hence 327 is the greatest among the four.
ANSWER:D
Answer: D