divelab/Sys2Bench huggingface dataset:
Question: There are 10 points on a circle. A hexagon can be formed by linking 8 of the 10 points. How many such hexagons are possible?
Options:
A)45
B)120
C)200
D)210
E)600
Rationale: 8 points can be selected out of 10 points in 10C8 ways
=10 !/8!*2!=45
Ans A
Answer: A
Question: A certain bus driver is paid a regular rate of $16 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 $1004 in total compensation, how many total hours did he work that week?
Options:
A)36
B)40
C)44
D)48
E)53
Rationale: For 40 hrs = 40*16=640
Excess = 1004-640=364
For extra hours =.75(16)=12+16=28
Number of extra hrs =364/28=13
Total hrs =40+13=53
Answer E 53
Answer: E
Question: Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
Options:
A)38
B)31
C)41
D)None of these
E)Cannot be determined
Rationale: Explanation :
Let there be x mints originally in the bowl.
Sita took 1/3 but returned 4. So, noe the bowl haa (2x/3) + 4 mints
Fatima took 1/4 of the remainder but returned 3. So, the bawl now has (3/4)((2x/3) + 4) + 3 mints.
Eshwari took half of the remainder that is (1/2) [ (3/4) ( (2x/3) + 4 ) + 3 ]
She returns 2, so the bawl now has
=> (1/2) [ (3/4) ( (2x/3) + 4) + 3 ] + 2 = 17.
=> x = 48.
Answer : D
Answer: D
Question: How many liters of water must be evaporated from 50 liters of a 4-percent sugar solution to get a 10-percent solution?
Options:
A)30
B)32
C)34
D)36
E)38
Rationale: 4% of a 50 liter solution is 2L which is 10% of the solution at the end.
The solution at the end must be 20 L.
We need to evaporate 30 liters.
The answer is 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)21
C)22
D)23
E)24
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) + 62 = 16P => P = 17.
ANSWER:A
Answer: A
Question: In a certain furniture store, each week Nancy earns a salary of $240 plus 5% of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week ?
Options:
A)$2,200
B)$3,450
C)$4,200
D)$4,250
E)$5,000
Rationale: 450 = 240 + (5/100)*(Total Sales - 800)
i.e. (Total Sales - 800) = 20*(450-240) = 20*210 = 4200
i.e. Total Sales = 4200 + 800 = 5000
Answer: Option E
Answer: E
Question: If B + A < B - A < A - B, which of the following is correct?
Options:
A)A<B<0
B)B<A<0
C)B<0<A
D)0<B<A.
E)B>A>0.
Rationale: Check first inequality
B + A < B - A
A<-A
A is -ve
Check another equality
B - A < A - B
-2A<-2B
A>B
Combining both 0>A>B
Option B fits only
Ans B
Answer: B
Question: 80,873,72,72,64,81,56,?
Options:
A)96
B)98
C)89
D)90
E)88
Rationale: odd place numbers 80, 72, 64, 56 are divisible by 8.
even place numbers 873, 72, 81 are divisible by 9,so required number is in even place, from options 90 is only value visible by 9, so 90 is the answer.
ANSWER:D
Answer: D
Question: What is the sum of all the numbers between 300 and 1000 which are divisible by 179?
Options:
A)2506
B)2550
C)2450
D)3000
E)3500
Rationale: 358/179 â€¦.. 895/179
179(2 + 3 + 4 + 5) => 2506
ANSWER A
Answer: A
Question: A table is bought for Rs.600/- and sold at a loss of 12% find its selling price
Options:
A)s.500/-
B)s.530/-
C)s.528/-
D)s.600/-
E)s.700/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
88 % ------> 528 (88 * 6 = 528)
Selling price = Rs.528/-
C
Answer: C
Question: Two Equal Amounts of Money are lent out at 6% and 5 % simple Interest respectively at the same time. The former is recovered two years earlier than the latter and the amount so recovered in each case is Rs.2800. Determine the amount that is lent out?
Options:
A)3348
B)368
C)37077
D)1750
E)2701
Rationale: Explanation:
Let the first amount lent for t + 2 years and second at t years. and amount = P
Now amount = P + P×t×6100P×t×6100 = P×(t+2)×5100P×(t+2)×5100 = 2800.
Equating first two parts, we get t×6100=(t+2)×5100t×6100=(t+2)×5100
⇒ t = 10.
Now P+P×10×6100=2800P+P×10×6100=2800
⇒ 1610P=28001610P=2800
⇒ P = 1750.
Answer: D
Answer: D
Question: Three sets of 40, 50 and 60 students appeared for an examination and the pass percentage was 50, 90 and 75 respectively. the pass percentage of the whole set is
Options:
A)73.33%
B)73.44%
C)74.33%
D)85.33%
E)71.33%
Rationale: Explanation:
total passed student =20+45+45=110
110 is 73.33% of 150
ANSWER:A
Answer: A
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
Options:
A)1:2
B)3 : 4
C)1:4
D)2:5
E)3:7
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Answer: B
Question: the sum of 4th and 20th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0
Options:
A)10
B)7
C)11
D)5
E)3
Rationale: t4 + t20 = t8 + t15 + t12
=> a+3d + a+19d = a+7d + a+14d + a+11d
=> a + 10d = 0
=> t11 = 0 i.e. 11th term is zero.
ANSWER: C
Answer: C
Question: Train A & B leave from same station and reaches same destination but train A leaves half an after Train B & travels 2 times faster than B. Total distance is 100 miles & train B travels 50 miles/hour. Which train reaches the destination first & what is the time difference between the train
Options:
A)Train A reaches 30 minutes before Train B
B)Train B reaches 30 minutes before Train A
C)Train A reaches 60 minutes before Train B
D)Train B reaches 60 minutes before Train A
E)None of the above
Rationale: Time taken for train A = 30 minutes + d1/s1 = 30 minutes + 100 / 100 = 1 hours 30 minutes
Since Train B travels 50 miles / hour ; train A travels twice the speed of B which gives s1 = 100 miles/ hour
Time taken for train B = d2/s2 = 100 / 50 = 2 Hours
So Train A reaches 30 minutes before Train B
Answer: A
Answer: A
Question: Seven children â€” A, B, C, D, E, F, and G â€” are going to sit in seven chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
Options:
A)600
B)720
C)1440
D)4320
E)4800
Rationale: There are six different pairs of â€œnext to each otherâ€ chairs. For each pair, children C & F could be in either order, so thatâ€™s 6*2 = 12 possibilities for these two.
Now, consider the other five children. For any configuration of C & F, the remaining five children could be seated in any order among the five remaining seats. Five items in any order â€” thatâ€™s a permutation of the 5 items â€”- 5P5 = 5! = 120. For any single configuration of C & F, there are 120 ways that the other children could be seated in the remaining seats.
Finally, weâ€™ll combine with the Fundamental Counting Principle. We have 12 ways for the first two, and 120 ways for the remaining five. Thatâ€™s a total number of configurations of 12*120 = 1440. Answer = C
Answer: C
Question: Find the odd man out. 18, 27, 36, 38, 45
Options:
A)18
B)27
C)36
D)45
E)38
Rationale: All numbers except 38 are multiples of 9
Answer is E
Answer: E
Question: If 222 = 6
333 = 12
444 = 20
Then, 555 = ??
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: 222=2*2+2=6
333=3*3+3=12
444=4*4+4=20
555=5*5+5=30
ANSWER:A
Answer: A
Question: A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?
Options:
A)28
B)57
C)58
D)83
E)73
Rationale: Explanation:
2 *3(15 + 4) = 114
114 * 1/2 = Rs.57
Answer: Option B
Answer: B
Question: If a2 + b2 + c2 = 281 and ab + bc + ca =4, then a + b + c is
Options:
A)16
B)18
C)22
D)17
E)20
Rationale: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 281 and ab + bc + ca = 4,
(a + b + c)^2 = 281 + 2(4)
= 289
= 17^2
therefore: a + b + c = 17
ANSWER:D
Answer: D
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 2 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
Options:
A)1/15
B)1/5
C)4/15
D)3/10
E)2/5
Rationale: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=2(1/5(x/2))=2/10(x)--->non major=x/2-2/10(x)=3/10(x)
hence 3/10
D
Answer: D
Question: How many integers between 400 and 1000 are there such that their unit digit is odd?
Options:
A)250
B)150
C)300
D)400
E)450
Rationale: There are 600 numbers from 401 to 1000 (inclusive).
Half of the numbers are odd, so there are 300 odd numbers.
The answer is C.
Answer: C
Question: Divide $450 among A,B in the ratio 1:4. How many $ that A get?
Options:
A)$90
B)$500
C)$150
D)$250
E)$600
Rationale: Sum of ratio terms = 1+4 = 5
A = 450*1/5 = $90
Answer is A
Answer: A
Question: If 16,666 – n is divisible by 11, and 0 < n < 11, what is n?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 16,666 / 11 = 1515 with a remainder of 1.
We need to subtract the remainder to get a multiple of 11.
The answer is A.
Answer: A
Question: If 3f+ 1 < 2f < 9 - f, which of the following must be true?
I. -1 < f < 3
II. f < -1
III. f < 3
Options:
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
Rationale: Just try plugging f in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.
So you can immediately cross out any answers with I or III, leaving just (A) II only.
Answer: A
Question: ((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)
What is m?
Options:
A)17
B)18
C)34
D)31
E)36
Rationale: ((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)
((1/5)^m ) * ((1/2)^32) = 1/ (2 * (2*5)^31))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^m= (1/5)^31
((1/5)^m ) * ((1/2)^32) = 1/[(2^32)*(5^31)]
So, m=31
Answer D
Answer: D
Question: Two trains 150 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)10.7
B)10.9
C)10.26
D)11.16
E)18.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 150 + 160 = 310 m.
Required time = 310 * 9/250 = 11.16 sec.
Answer:D
Answer: D
Question: How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?
Options:
A)4
B)5
C)9
D)10
E)11
Rationale: Number of positive multiples of 5 less than 60 = 11
5*1=5
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5*7=35
5*8=40
5*9=45
5*10=50
5*11=55
Only 5 of the above are a product of a positive multiple of 5 and an even number - 10,20,30,40,50
Answer B
Answer: B
Question: In what time will a train 120 m long cross an electric pole, it its speed be 185 km/hr?
Options:
A)2.3 sec
B)2.9 sec
C)2.7 sec
D)8.7 sec
E)8.5 sec
Rationale: Speed = 185 * 5/18 = 51 m/sec
Time taken = 120/51 = 2.3 sec.
Answer: A
Answer: A
Question: How many positive three-digit integers are divisible by both 2 and 7?
Options:
A)40
B)46
C)52
D)64
E)70
Rationale: A number to be divisible by both 2 and 7 should be divisible by the least common multiple of 2 and 7 so by 14.
Multiples of 14 between 100 and 999, inclusive is
(last-first)/multiple+1=(994-112)/14+1=63+1=64
Answer: D.
Answer: D
Question: A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
Options:
A)1:5
B)625:3125
C)100:105
D)100^4:105^4
E)725:3225
Rationale: The interest earned in the 1st year = $500
The interest earned in the 2nd year = $500*1.05
The interest earned in the 3rd year = $500*1.05^2
The interest earned in the 4th year = $500*1.05^3
The interest earned in the 5th year = $500*1.05^4
(500*1.05^3)/(500*1.05^4) = 1/1.05=100/105.
Answer: C.
Answer: C
Question: There are 300 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
Options:
A)200
B)175
C)150
D)125
E)100
Rationale: There are 297 managers and 3 others. The 3 others would compose 2% of the total number of people if there were 150 people in the room. Thus 150 managers must leave.
The answer is C.
Answer: C
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=P+21, what is the perimeter of the garden in feet?
Options:
A)24
B)28
C)32
D)36
E)40
Rationale: Let x be the length of one side of the square garden.
x^2 = 4x + 21
x^2 - 4x - 21 = 0
(x-7)(x+3) = 0
x = 7, -3
P = 4(7) = 28
The answer is B.
Answer: B
Question: In a forest 10 rabbits were caught, tagged with electronic markers, then released. A month later, 10 rabbits were captured in the same forest. Of these 10 rabbits, it was found that 2 had been tagged with the electronic markers. If the percentage of tagged rabbits in the second sample approximates the percentage of tagged rabbits in the forest, and if no rabbits had either left or entered the forest over the preceding month, what is the approximate number of rabbits in the forest?
Options:
A)150
B)70
C)50
D)1,500
E)500
Rationale: Given that 10 rabbits were caught and tagged in the first sample, and 10 were caught in the second sample of which 2 had tags, then 2/10 approximates the fraction of the population of tagged rabbits in the forest.
Proportion: A/x = C/D
A = rabbits tagged first sample
C/D = the fraction of the population of tagged rabbits in the forest
x = the population of rabbits in the forest
Proportion: 10/x = 1/5
x = (1)(10)(5) = 50. There are approximately 50 rabbits in the forest.
Answer is C
Answer: C
Question: A and B started a business with initial investments in the ratio 14 : 15 and their annual profits were in the ratio 7 : 6. If A invested the money for 10 months, for how many months did B invest his money?
Options:
A)2
B)4
C)6
D)8
E)9
Rationale: Sol.
Suppose A invested Rs. 14x for 10 months and B invested Rs. 15x for y months. Then,
14x * 10 / 15x * y = 7/6 ⇒ y = 840 / 105 = 8
Hence, B invested the money for 8 months.
Answer D
Answer: D
Question: Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.?
Options:
A)8
B)12
C)14
D)16
E)18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+34
3x + 6 = x + 34
2x = 28
\inline \therefore x = 14
\inline \therefore Middle number = x + 2 = 14+2 = 16
D
Answer: D
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.18000. A's share is?
Options:
A)6028
B)6020
C)6000
D)6098
E)6008
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
Answer: C
Answer: C
Question: How many integers between 265,205and 758,805 have tens digit 1 and units digit 3?
Options:
A)4,629
B)4,639
C)3,946
D)4,926
E)4,936
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 265,205 and 758,805 is 758,805-265,205=493,600 - one number per each hundred gives 133,900/100=4,936 numbers.
Answer: E.
Answer: E
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 two 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)18:8
Rationale: Water:soap = 3:2
Soap:Salt=6:2
=> For 6 soap, salt = 2
=> For 2 Soap, salt = (2/6)*2 = 2/3
So, water:soap:salt = 3:2:2/3 = 18:12:4
After open container, water:soap:salt = 9:18:4
So, water:salt = 9:4 = 18:8
E
Answer: E
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $55,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
Options:
A)$10,000
B)$11,200
C)$12,000
D)$12,800
E)$19,800
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 40000 + (40000 - 20% of 40000) + 40% of (40000 - 20% of 40000)
= 52800
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 55000 + (55000 - 20% of 55000) + 40% of (50000 - 20% of 55000)
= 72600
Diff = 72600 - 52800 = 19800
Hence, E.
Answer: E
Question: If A, B, and C invested some amount in the ratio 3:2:5 in a buisiness. If the total profit incurrec after a year was Rs.12100, find the share of B.
Options:
A)Rs.6050
B)Rs.3630
C)Rs.2420
D)Rs.3360
E)Rs.6100
Rationale: Total profit after a year =12100 Ratio of profit share =3x+2x+5x=10x 10x = 12100. Therefore x=1210 B's share = 2*1210 =Rs.2420 Answer : C
Answer: C
Question: If an amount of Rs 13,640 is divided equally among
62 students, approximately how much amount will
each student get?
Options:
A)Rs 206
B)Rs 210
C)Rs 220
D)Rs 218
E)None
Rationale: Amount received by each student = 13640/62 â‰ˆ Rs
220
Answer C
Answer: C
Question: Three friends sai, vani and ram divide $1020 amongs them in such a way that if $10, $20 and $15 are removed from the sums that sai, vani and ram received respectively, then the share of the sums that they got will be in the ratio of 8 : 4 : 2. How much did ram receive?
Options:
A)$147
B)$142
C)$242
D)$122
E)$143
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 10 : y - 20 : z -15 is 8a : 4a : 2a
When $10, $20 and $15 are removed, we are removing a total of $45 from $1020.
Therefore, 8a + 4a + 2a = 1020 - 45 = 975
i.e., 14a = 975
or a = 70.
We know that z - 2 = 70a = 2 * 70 =140
Therefore, z = 140 + 2 = $142
The correct choice is (B)
Answer: B
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
Options:
A)38
B)39
C)40
D)46
E)49
Rationale: Let there be x pupils in the class.
Total increase in marks = (x x 1/2) = x/2
x /2 = (83 - 63)
x /2= 20
x= 40
Answer is C
Answer: C
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?
Options:
A)16
B)15
C)12
D)87
E)16
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s
= 12∏ cm.
Answer:C
Answer: C
Question: A train running at the speed of 90 km/hr crosses a pole in 6 seconds. What is the length of the train?
Options:
A)150
B)2766
C)187
D)267
E)191
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: A
Answer: A
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)32:47
B)32:49
C)32:45
D)32:46
E)32:41
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer: C
Answer: C
Question: In a graduate physics course, 60 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the female students is single?
Options:
A)2/7
B)17/30
C)1/2
D)27/40
E)5/7
Rationale: let assume there are 100 students of which 60 are male and 40 are females
if 30 are married then 70 will be single.
now its given that two-sevenths of the male students are married that means 2/7 of 60 = 17 males are married
if 30 is the total number of students who are married and out of that 17 are males then the remaining 13 will be females who are married.
total females = 40
married females = 13
then single females = 40-13 = 27
we need to find the fraction of female students who are single i.e single female students / total female student
= 27/40 [D]
Answer: D
Question: In how many ways, a committee of 5 members can be selected from 7 men and 5 ladies, consisting of 3 men and 2 ladies?
Options:
A)75
B)152
C)175
D)350
E)412
Rationale: (3 men out 7) and (2 ladies out of 5) are to be chosen
Required number of ways = (7C3 * 5C2) = 350
Answer is D
Answer: D
Question: Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 300 grams of compound X?
Options:
A)54
B)162
C)250
D)270
E)322
Rationale: total number of fractions =2+10=12
element B constitutes =10 out of 12 parts of X
So in 300 gms of X have 300*10/12=250 gms of B
and 300-250=50 gms of A.
cross check:- A/B = 50/250 =2/10 (as given)
Ans C
Answer: C
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 7 years hence?
Options:
A)58
B)74
C)62
D)70
E)74
Rationale: Explanation:
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
7 years, their ages will be 47 and 27.
Sum of their ages = 47 + 27 = 74.
B)
Answer: B
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)10%
B)11%
C)12%
D)15%
E)13%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
ANSWER:C
Answer: C
Question: Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 3 hours. How long would it take for both hoses to fill up two-thirds of the pool?
Options:
A)5/12 hours
B)5/8 hours
C)4/3 hours
D)12/7 hours
E)12/5 hours
Rationale: Hose 1 would fill the pool alone in 6 hours
i.e. 1 Hour work of Hose 1 = 1/6
Hose 2 would fill the pool alone in 3 hours
i.e. 1 Hour work of Hose 2 = 1/3
i.e. 1 Hour work of Hose1 and Hose2 together = (1/6)+(1/3) = (1/2)
i.e. (1/2) work can be finished by Hose1 and Hose2 together in 1 hour
i.e. (2/3) work can be finished by Hose1 and Hose2 together in 1*(2)*(2/3) = 4/3 hour
Answer: Option C
Answer: C
Question: 10^185 - 10^9 = Which of the following best approximates the value of the expression above?
Options:
A)10^170
B)10^180
C)10^(185)
D)10^160
E)10^179
Rationale: 10^185 - 10^9 =
Which of the following best approximates the value of the expression above?
Yes, answer 10^185 is correct. Note that we need approximate value of the given expression and as 10^(185) is much larger number than 10^(9) then 10^(9) is pretty much negligible in this case: 10^(185)-10^(9)=~10^(185).
Answer : C
Answer: C
Question: 45 pupil,out of them 12 in debate only and 22 in singing only.then how many in both?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: The intersection for two = 45 - 12 - 22 = 11 play both games.
ANSWER:C
Answer: C