divelab/Sys2Bench huggingface dataset:
Question: On Saturday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
Options:
A)Tuesday
B)Wednesday
C)Thursday
D)Friday
E)Saturday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Saturday, 3rd day is Tuesday. Next day, which he won't have a new combination for, is Wednesday. (B)
Answer: B
Question: On January 1, 2011, Dimple invests 20% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 50% in Antarctic smallcaps. In 2011, largecaps rise 20%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2013, Dimple has the same total amount of retirement savings as he did two years before, then x is between
Options:
A)0 and 5
B)5 and 10
C)10 and 15
D)15 and 20
E)20 and 30
Rationale: Pick a smart number for the total retirement savings Dimple starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.)
Here are the starting values:
L = $2000
M = $3000
S = $5000
Apply the first year’s changes, so that you have these numbers on 1/1/2012:
Newer L = $2000+ 20% = $2400
Newer M = $3000+ 10% = $3300
Newer S = $5000+ 20% = $6000
Now apply the second year’s changes to L and M:
Newest L = $2400– 10% = $2400– $240 = $2160
Newest M = $3300– 20% = $3300– $660= $2640
Add these to get $4800. So the newest S must be $10,000 (the target final total of Dimple’s retirement savings) minus $4800, $5200
The dollar change in S from 1/1/12 to 1/1/13 is $6000 – $800 = $5200. So the question is this: what percent change does $800 represent, from a starting point of $6000? Since $6000 is a nasty divisor, switch to benchmarks:
5% of $6000 = $300.
10% of $6000 = $600.
15% of $6000 = $900.
And so on.
From this $800 lies between $600 and $900
The correct answer is C.
Answer: C
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: A
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 34 years. What is Deepak present age?
Options:
A)22
B)15
C)77
D)21
E)182
Rationale: Present age is 4x and 3x,
=> 4x + 6 = 34 => x = 7
So Deepak age is = 3(7) = 21
Answer: D
Answer: D
Question: If the sides of a triangle are 26 cm, 24 cm and 12 cm, what is its area?
Options:
A)144
B)772
C)288
D)266
E)2848
Rationale: The triangle with sides 26 cm, 24 cm and 12 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 12 = 144 cm2
Answer: A
Answer: A
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/6%
B)16 9/3%
C)19 2/9%
D)16 2/3%
E)16 7/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes.How long will it take to go 5 km in stationary water ?
Options:
A)40 minutes
B)1 hour
C)1 hr 15 min
D)1 hr 20 min
E)None of these
Rationale: Solution
Rate downstream =(1/10x60) km/hr = 6 km/hr, Rate upstream = 2 km/hr.
Speed in still water =1/2(6 + 2) km/hr = 4 km/hr.
∴ Required time =(5/4)hrs = 1 1/4hrs = 1 hr 15 min. Answer C
Answer: C
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
Options:
A)150
B)152
C)158
D)159
E)150
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
C
Answer: C
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Options:
A)276
B)299
C)322
D)345
E)355
Rationale: Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322. Answer: Option C
Answer: C
Question: a spider web consists of 3 concurrent lines forming radial support for 20 concentric regular hexagon .the hexagon vertices are 5mm from their immidiate neighbour. if the innermost hexagon has a side length 3mm how many meters is the length of the entire web including the 3 diagonals ?
Options:
A)7.354 m
B)8.354 m
C)6.354 m
D)9.354 m
E)5.354 m
Rationale: for perimeter of all hexagon =6*(3+8+13+...........20th term.)
sum will be 6060 mm
and for length of one diagonal find 20th term=98
so total length =6060+294=6354 mm=6.354 m
ANSWER:C
Answer: C
Question: David obtained 86, 85, 82, 87 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
Options:
A)75
B)276
C)87
D)85
E)11
Rationale: Explanation:
Average = (86+ 85+ 82+ 87+ 85 )/ 5 = 425/5 = 85.
Answer:D
Answer: D
Question: consider a no 235, where last digit is the sum of first two digit no eg- 2+3=5 , how many such 3-digit no are there ???
Options:
A)44
B)45
C)46
D)47
E)48
Rationale: between 100 and 200 there are 9 such numbers
101,112,123,134,145,156,167,178,189
in the same way btwn 200 and 300
202,213,224,235,246,257,268,279 =8 numbers totally
so series continues as 9+8+7+6+5+4+3+2+1=45 numbers
ANSWER:B
Answer: B
Question: If the integer w is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when w is rounded to the nearest ten. which of the following is a possible value of w?
Options:
A)64
B)67
C)99
D)133
E)147
Rationale: We have to check options 1 by 1.
64 rounded to nearest hundred = 100
64 rounded to nearest ten = 60
now difference = 40
the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.
therefore 40/60)*100 = 66 2/3 ==>this is the answer.
99 rounded to nearest ten = 100
133 rounded to nearest ten = 130
133 rounded to nearest hundred w= 100=A
Answer: A
Question: If Rahul earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased?
Options:
A)1/4
B)1/5
C)1/10
D)9/100
E)1/20
Rationale: Perhaps it is also easy to just translate the % into fractions:
6%: 6/100 = 3/50
7%: 7/100
8%: 8/100 = 4/50 =2/25
9%: 9/100
Only 9/100 exists in the answer choices, so ANS D
Answer: D
Question: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 5.00 a.m., at what time will he first touch a flag at 120 feet from the ground?
Options:
A)4 p.m.
B)5 p.m.
C)6 p.m.
D)7 p.m.
E)3 p.m
Rationale: Explanation:
Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.
So, the monkey ascends 90 feet in 9 hours i.e. till 2 p.m.
Clearly, in the next 1 hour i.e. till 3 p.m. the monkey ascends remaining 30 feet to touch the flag.
Answer:E
Answer: E
Question: Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 10 complete revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 9 more revolutions than gear L?
Options:
A)a) 6
B)b) 8
C)c) 10
D)d) 18
E)e) 15
Rationale: Gear L -- 10 rotations per 60 seconds -- 1 rotation per 6 seconds.
Gear R -- 40 rotations per 60 seconds -- 4 rotations per 6 seconds.
First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference -- 3 rotations
Hence every 6 seconds the difference between the number of rotations of R and L gear is 3 units.
Required net difference should be 9 rotations => 3 (6 seconds later) ==> 18 seconds.
Answer: D).
Answer: D
Question: Tom is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 powder , and the remainder an even mixture of salt, pepper and sugar. If Tom accidentally doubles the powder and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
Options:
A)15/29
B)5/8
C)5/16
D)1/2
E)13/27
Rationale: Olive oil = 5/8 = 15/24 --> 15 parts out of 24;
powder = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;
If powder = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion = 15/29.
Answer: A.
Answer: A
Question: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4?
Options:
A)1/5
B)1/20
C)4/5
D)7/3
E)2/7
Rationale: If a number is divisible by 4 the last 2 digits of the number has to be divisible by 4.
If the number ends with 12: Number of possibilities = 2 * 1 = 2
number ends with 24: Possibilities =2 * 1 = 2
number ends with 32: Possibilities = 2
Total number of possibilities with restriction = 2+2+2=6
Total number of possibilities without restriction = 5! = 120
Probability = 6/120 = 1/20
Answer:B
Answer: B
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 108 grams of compound X?
Options:
A)90
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 108 gms of X have 108*10/12=90 gms of B
and 108-90=18 gms of A.
cross check:- A/B = 18/90 =2/10 (as given)
Ans A
Answer: A
Question: Mike's age is 48 years. If he is 4 more than twice the age of his son, find the age of his son.
Options:
A)20 years
B)22 years
C)16 years
D)18 years
E)19 years
Rationale: Let Mike's son age be x.
4 + 2 x = 48
x = 22
Hence Mike's son age is 22 years
Answer : B
Answer: B
Question: 50, 47, 45, 42, 40, 37, 35, 32, ?
Options:
A)31
B)30
C)29
D)28
E)27
Rationale: This is an alternating number subtraction series. The pattern is -3, -2, -3, -2, ....
The answer is B.
Answer: B
Question: HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 20%
Options:
A)36
B)40
C)32
D)42
E)60
Rationale: (x+30)*30=(120/100)(25x+30*30)
Solving we get 60.
Answer is E.
Answer: E
Question: A and B started a business with initial investments in the ratio 10 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?
Options:
A)6 months
B)8 months
C)9 months
D)35 months
E)7 months
Rationale: Let Sumit in the business for ‘a’ months.
Investment Ratio Amit to Sumith = 10:3
Profit sharing ratio = 8 : 7.
Amit is in the business for 12 months.
Then Sumit in the business for
(10 × 12) / (3 × a) = 8 / 7 => 24a = 840 or
a = 840 / 24 = 35 or 35 months
Option D
Answer: D
Question: At the opening of a trading day at a certain stock exchange, the price per share of stock K was $28. If the price per share of stock K was $29 at the closing of the day, what was the percent increase in the price per share of stock K for that day?
Options:
A)3.57%
B)5.9%
C)11.1%
D)12.5%
E)23.6%
Rationale: Opening = 28
Closing = 29
Rise in price = 1
So, percent increase = 1/28*100 = 3.57
Answer : A
Answer: A
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Options:
A)2668
B)9261
C)1688
D)2588
E)1611
Rationale: Explanation:
A = 8000(21/20)3 = 9261
Answer:B
Answer: B
Question: Two air planes are moving in the same direction at 29 kmph and 11 kmph. The faster air plane crosses the slower air plane in 10 seconds. Find the length of the faster air plane in meters.
Options:
A)36 m
B)71 m
C)42 m
D)50 m
E)59 m
Rationale: Relative speed = (29 - 11) * 5/18 = 5 = 5 mps.
Distance covered in 27 sec = 10 * 5 = 50 m.
The length of the faster train = 50 m.
Answer:D
Answer: D
Question: How many 4-digit numbers can be formed from the digits 0,2, 3, 5, 6, 7 and 9, which are divisible by 5 and if the repetition is not allowed?
Options:
A)200
B)240
C)300
D)360
E)120
Rationale: Since, each desired number is divisible by 5, so we must have either 0 or 5 at the unit place.
So , the tens place can now be filled by any of the remaining 6 digits (2, 3, 6, 7, 9, 0 or 5)
the hundreds place can now be filled by any of the remaining 5 digits
therefore the 3-digit no can be formed by (4 * 5 * 6 * 2) = 240 ways
Ans- B
Answer: B
Question: Two friends want to buy a snack. They combine their money and find they have $3.75, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Let x be the number of quarters. Then 2x is the number of nickels.
(1) 25x + 10x + 10D = 375. Then 7x + 2D = 75
(2) 3x + D = 35. Then 6x + 2D = 70
Let's subtract equation (2) from equation (1).
x = 5
The answer is B.
Answer: B
Question: Find the sum of all 2 digit numbers divisible by 3.
Options:
A)1665
B)1765
C)1865
D)1965
E)1555
Rationale: All 2 digit numbers divisible by 3 are :
12, 51, 18, 21, ..., 99.
This is an A.P. with a = 12 and d = 3.
Let it contain n terms. Then,
12 + (n - 1) x 3 = 99 or n = 30.
Required sum = 30/2 x (12+99) = 1665.
Answer is A
Answer: A
Question: Three sets of 80, 50 and 90 students appeared for an examination and the pass percentage was 75, 90 and 100 respectively. the pass percentage of the whole set is
Options:
A)87.63%
B)88.53%
C)88.93%
D)88.63%
E)89.63%
Rationale: Explanation:
total passed student =60+45+90=195
195 is 88.63% of 220
ANSWER:D
Answer: D
Question: P is a no. which has exactly 3 factors which divide 25! Then whats is the greatest power of 3 in (p-25)!
Options:
A)46
B)47
C)48
D)49
E)50
Rationale: suppose p=125 has three factor 125==5*5*5;
(125-25)=100;
power of 3=100/3=33.33/3+11.11/3+3.3/3=47+11+3+1=48
ANSWER:C
Answer: C
Question: A, B and C start a business each investing 20,000. After 10 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 71400 was recorded. Find the share of B.
Options:
A)20,000
B)21,200
C)23,200
D)20,500
E)None of these
Rationale: Ratio of the capitals of A, B and C
= 20000 Ã— 10 + 15000 Ã— 2 : 20000 Ã— 10 + 16000 Ã— 2 : 20000 Ã— 10 + 26000 Ã— 2
= 230000 : 232000 : 252000 = 230 : 232 : 252.
Bâ€™s share = (71400 Ã— 232â„714) = 23200;
Answer C
Answer: C
Question: Find the compound interest on Rs. 16,000 at 20% per annum for 9 months, compounded quarterly
Options:
A)2875
B)2654
C)2645
D)2456
E)2522
Rationale: Principal = Rs. 16000; Time = 9 months =3 quarters;Rate = 20% per annum = 5% per quarter.Amount = Rs. [16000 x (1+(5/100))3] = Rs. 18522. CI. = Rs. (18522 - 16000) = Rs. 2522 Answer : E
Answer: E
Question: If point A coordinates are (-7, -2) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
Options:
A)(-2, - 2/3)
B)(2, -2/3)
C)(2/3, -2)
D)(0, 2)
E)(2, 2/3)
Rationale: Look at the diagram below:
Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-7+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be D.
Answer: D.
Answer: D
Question: The value of (10^9-10^2)/(10^7-10^3) is closest to which of the following?
Options:
A)1
B)10
C)10^2
D)10^3
E)10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^9 - 10^2
10^9 is HUGE compared to 10^2.
So 10^9 - 10^2 is very close to 10^9 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^7 is HUGE compared to 10^3.
So 10^7 - 10^3 is very close to 10^7.
So we have:
10^9/10^7
or 10^(9-7) = 10^2.
Choose C.
Answer: C
Question: If g(x) = ax^5 + bx^3 + 3, and g(5) = 10, then g(–5) =?
Options:
A) – 10
B) – 8
C) – 6
D) 0
E) -4
Rationale: g(5) = 10
or, 5^5 a + 5^3 b + 3 = 10
or, 5^5 a + 5^3 b = 7
g(-5) = -5^5 a - 5^3 b + 3 = - (5^5 a + 5^3 b) + 3 = - 7 + 3 = - 4 = (E)
Answer: E
Question: At Veridux Corporation, there are 218 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?
Options:
A)15
B)20
C)25
D)30
E)47
Rationale: Well, first letâ€™s take care of the â€œtotalsâ€. The numbers in the â€œtotalsâ€ row must add up. If 90 are females, the other 218 â€“ 90 = 128 must be males. Similarly, the numbers in the â€œtotalsâ€ column must add up. If 40 are managers, then the other 218 â€“ 40 = 178 must be associates.
Now, in the â€œassociateâ€ row, 135 + E = 178, which means E = 43 â€” the other 43 associates must be female.
Now, to find B, which is what the question is asking, we need only look at the sum in the â€œfemaleâ€ column: B + 43 = 90, which means B = 47. There are fifteen female managers in this company. Thus, the answer = 47 (E).
Answer: E
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 4 rounds per hour respectively. If they start at 7 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.00 a.m.?
Options:
A)10
B)6
C)12
D)8
E)16
Rationale: Relative speed = Speed of A + Speed of B (âˆ´ they walk in opposite directions)
= 2 + 4 = 6 rounds per hour
=> They cross each other 6 times in 1 hour.
Time duration from 7.00 am to 9.00 am = 2 hour
Hence they cross each other 12 times before 9.00 am
Answer : C
Answer: C
Question: A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 800 square feet, what is the total length of the fence, in feet?
Options:
A)40
B)80
C)100
D)120
E)200
Rationale: two sides EACH = x the third = 2x and the wall length is thus 2x too
x*2x = 2x^2 = 800 ie x^2 = 400 ie x = 20
L = 40 W= 20
TOTAL LENGTH OF FENCE = 2*20+ 40 = 80
MY ANSWER IS B
Answer: B
Question: A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is?
Options:
A)298 m
B)188 m
C)240 m
D)178 m
E)189 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 12
= 240 m.
Answer:C
Answer: C
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)132
B)240
C)188
D)111
E)123
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m
Answer: B
Answer: B
Question: 54 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
Options:
A)33
B)66
C)18
D)100
E)281
Rationale: (54 * 8)/30 = (x * 6)/50 => x =120
120 – 54 = 66
Answer: B
Answer: B
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 10 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
Options:
A)$10,350
B)$10,395
C)$10,890
D)$11,500
E)$12,705
Rationale: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10890. So the answer is (C).
Answer: C
Question: Village X has a population of 70000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?
Options:
A)14
B)19
C)11
D)18
E)13
Rationale: Let the population of two villages be equal after p years
Then, 70000-1200p=42000+800p
2000p=28000
p=14
Answer is A.
Answer: A
Question: 35% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
Options:
A)25%
B)35%
C)45%
D)55%
E)65%
Rationale: To maximize the percentage of companies offering both, let's assume that all 35% of companies which offer wireless internet also offer snacks.
The answer is B.
Answer: B
Question: Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 54, how many more green disks than blue disks are in the bag?
Options:
A)15
B)25
C)30
D)35
E)40
Rationale: Let B:Y:G = 3x:7x:8x.
3x + 7x + 8x = 18x = 54 --> x= 3.
G - B = 8x - 3x = 5x = 15.
The answer is A.
Answer: A
Question: In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Options:
A)266
B)5040
C)11760
D)86400
E)None
Rationale: Required number of ways	= (8C5 x 10C6)
= (8C3 x 10C4)
= (8 x 7 x 6)/(3x2x1)	x	(10 x 9 x 8 x 7	)/(4x3x2x1)
= 11760.
Option C
Answer: C
Question: How many litres of water must be added to 16 liters of milk and water contains 10% water to make
it 20% water in it
Options:
A)4 litre
B)2 litre
C)1 litre
D)3 litre
E)None of these
Rationale: Explanation :
By the rule of alligation, we have
% Concentration of water
in pure water : 100 % Concentration of water
in the given mixture : 10
Mean % concentration
20
20 - 10 = 10 100 - 20 = 80
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here Quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
Quantity of water = 16×18=2 litre
Answer : Option B
Answer: B
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 6 km in stationary water?
Options:
A)40 minutes
B)1 hour
C)1 hour 15 min
D)1 hour 30 min
E)1 hour 10 min
Rationale: speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(10/60)= 6 kmhr
speed in still water = 1/2 (2+6) = 4 kmhr
time taken in stationary = 6/4 = 1 hrs 30 min
ANSWER:D
Answer: D
Question: There are 3 teams each with 3 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
Options:
A)50
B)23
C)27
D)28
E)45
Rationale: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 9 possibilities (3*3) since each team has 3 players. So there are a total of 27 possibilities (9*3). I hope this method is easier for you to understand.
Answer: C
Question: Fill in the blank with the correct number in this number series: 1, 20, 7, 16, __, 12, 19, ?
Options:
A)14
B)12
C)13
D)15
E)11
Rationale: This is a simple alternating subtraction and addition series; The first series begins with 1 and adds 6; the second begins with 20 and subtracts 4, and so on.
Answer: C
Answer: C
Question: Find the number of ways of arranging a pen and 6 pencils at a circular table so that the pen always sits in a particular place?
Options:
A)3!
B)6!
C)11!
D)12!
E)14!
Rationale: Ans.(B)
Sol. Total number of persons = 7. The pen can sit in a particular place in one way. Now, remaining positions are defined relative to the pen. Hence, the remaining can sit in 6 places => 6! Ways ... The number of required arrangements = 6! x 1= 6! = 6! ways
Answer: B
Question: What decimal of an hour is a second ?
Options:
A).0025
B).0256
C).00027
D).00016
E).000126
Rationale: Required decimal =	1/(60x60)
=	1/3600
= .00027
answer :C
Answer: C