divelab/Sys2Bench huggingface dataset:
Question: If a is a positive integer, and if the units digit of a^2 is 4 and the units digit of (a+1)^2 is 9, what is the units digit of (a+2)^2?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: If the units digit of a^2 is 4, then the units digit of a is either 2 or 8.
If the units digit of (a+1)^2 is 9, then the units digit of a+1 is either 3 or 7.
To satisfy both conditions, the units digit of a must be 2.
Then a+2 has the units digit of 4, thus the units digit of (a+2)^2 will be 6.
The answer is D.
Answer: D
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
Options:
A)1278
B)1900
C)2888
D)2771
E)2322
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: B
Question: You have 5 sticks of lengths 20, 30, 40, 50, and 60 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is
Options:
A)3
B)6
C)7
D)10
E)12
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Based on this there can be only 7 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60).
Answer; C
Answer: C
Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is
Options:
A)20
B)23
C)27
D)150
E)255
Rationale: Explanation:
We know
(x+y)2=x2+y2+2xy
=>(x+y)2=289+2(120)
=>(x+y)=529−−−√=23
Option B
Answer: B
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 80% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
Options:
A)1.8 lakh
B)1.4 lakh
C)1.9 lakh
D)8.1 lakh
E)6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.8 = 5.4 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 5.4 - 1.2 = 4.2 lakh
Average SP of all the 3 cars = 1.4 lakh
Answer: B)
Answer: B
Question: The Reserve Bank of India will transfer its surplus profit of 65,896 crore rupees to the Centre. This amount is ___ percent higher than previous year.
Options:
A)25%
B)29%
C)35%
D)28%
E)65%
Rationale: ANSWER: A
Answer: A
Question: S1 = 2
S2 = 5
...
Sn = 3n + 4
For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?
Options:
A)13
B)12
C)14
D)11
E)16
Rationale: term 16 = 3*16+4 = 52
Answer : E
Answer: E
Question: If w>0, which of the following must be true?
Options:
A)1 < w
B)0 <w < 2
C)-1 < w < 1
D)-10 < w
E)1/100 < w
Rationale: All we know is that w is some positive number. Right away we can see that D must be true: if w is positive then it MUST be true that it's greater than -10. Still let's check each option.
A. 1 < w. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.
B. 0 < w < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.
C. -1 < w < 1. The same as A. Discard.
E. 1/100 < w. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.
Answer: D.
Answer: D
Question: A and B go around a circular track of length 300 m on a cycle at speeds of 18 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)120 sec
B)198 sec
C)60 sec
D)665 sec
E)276 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 300/ (90 * 5/18) , 300/ (54 * 5 /18) }
= LCM (12, 20) = 60 sec.
Answer:C
Answer: C
Question: How is 1% expressed as a decimal fraction?
Options:
A)0.1
B)0.001
C)0.01
D)0.0001
E)1
Rationale: 1/100= 0.01
ANSWER:C
Answer: C
Question: The average age of three boys is 40 years and their ages are in proportion 6:10:8. What is the age in years of the youngest boy?
Options:
A)8
B)10
C)7
D)6
E)5
Rationale: 6x + 10x + 8x = 40
x =1.6
6x = 10
Answer:B
Answer: B
Question: In a company, 48 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
Options:
A)85%
B)80%
C)75%
D)70%
E)65%
Rationale: The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
52% of all employees are women, so non-union women are 52%-18% = 34%
40% of all employees are non-union.
The percent of non-union employees who are women is 34%/40% = 85%
The answer is A.
Answer: A
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)17 km/hr
B)50 km/hr
C)76 km/hr
D)55 km/hr
E)51 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x
= 50 km/hr.
Answer: B
Answer: B
Question: 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8.
What is half of that number?
Options:
A)315
B)310
C)314
D)318
E)319
Rationale: Let the number be x. then 4/15 of 5/7 of x-4/9 of 2/5 of x=8<=>4/21x-8/45x=8
<=>(4/21-8/45)x=8<=>(60-56)/315x=8<=>4/315x=8
x=(8*315)/4=630<=>1/2x=315
Answer is A.
Answer: A
Question: A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $168, how many hours overtime did he work?
Options:
A)8
B)5
C)9
D)6
E)10
Rationale: Ans is A
At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $168 - $120 = $48 Overtime rate (twice regular) = 2 x $3 = $6 per hour => number of overtime hours = $48/$6 = 8
Answer: A
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?
Options:
A)15hr 10min
B)16hr 20min
C)2hr 48min
D)15hr
E)14hr 25min
Rationale: Work done by the leak in 1 hour = 1/2 - 1/7 = 5/14
Leak will empty the tank in 14/5 hrs = 2hr 48min
Answer is C
Answer: C
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 500 more than that by the previous schema, his sales were worth?
Options:
A)s. 14,000
B)s. 12,000
C)s.16,000
D)s. 40,000
E)s. 50,000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 16000
ANSWER:C
Answer: C
Question: A ring x of diameter 16 inches is placed inside another ring y of diameter of 18 inches. How much fraction of the ring x surface is not covered by the ring y?
Options:
A)13/15
B)12/4
C)16/17
D)22/16
E)17/81
Rationale: The questions asks us to find the surface which is not covered by the ring x i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem
Area of the ring x=pi* r^2, where r=8
=>pi*64
Area of the ring y=pi*81
Surface not covered by the ring x=pi*81-pi*64=Pi*17
fraction of ring y's surface is not covered by a ring x= Pi*17/total area of the ring y
=>Pi*17/Pi*81
17/81
Answer E
Answer: E
Question: On dividing 21 by a number, the quotient is 10 and the remainder is 1. Find the divisor.
Options:
A)1
B)2
C)4
D)6
E)7
Rationale: d = (D-R)/Q
= (21 - 1)/10
= 20/10 = 2
B
Answer: B
Question: Soniya deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Options:
A)9680
B)9850
C)9745
D)9623
E)9324
Rationale: (8000*3*2)/100 = 480
9200
--------
9680
ANSWER A
Answer: A
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)Rs.1000
B)Rs.1029
C)Rs.1028
D)Rs.1007
E)Rs.1297
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: A
Question: 6 college friends go on vacation together during spring break. Their rental house costs $1250. If each friend pays the same amount and no one has bills smaller than $1, how much money do they pay for the rental?
Options:
A)$1250
B)$1251
C)$1252
D)$1253
E)$1254
Rationale: In order to divide the sum in 6 parts, the amount must be divisible by 6.
Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
We need to make this number even in order for it to be divisible by 2.
Sum of digits of 1250 = 8 and 12 is divisible by both 3 and yields an even number.
Hence, we need to add 4 to this number for it to be divisible by 6
Correct Option: E
Answer: E
Question: 30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there?
Options:
A)800
B)1000
C)1200
D)1500
E)1800
Rationale: 800score Official Solution:
People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers.
Fishermen = (300 / 30) × 100 pers. = 1000 pers.
The correct answer is choice (B).
Answer: B
Question: There are two concentric circles with radii 5 and 4. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase?
Options:
A)56
B)156
C)256
D)356
E)456
Rationale: The area of a circle is piR^2, where R is the radius.
The area of the big circle is 25pi.
The area of the small circle is 16pi.
The area A1 between the circles is 9pi.
When the big circle's radius increases, the new area is 36pi.
When the small circle's radius decreases, the new area is 4pi.
The area A2 between the circles is 32pi.
The ratio of A2/A1 is 32/9 = 3.56 which is an increase of 256%.
The answer is C.
Answer: C
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 1. If p is any prime number then f(p)
Options:
A)p-1
B)p-2
C)(p+1)/2
D)(p-1)/2
E)2
Rationale: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-2=5.
Answer: B.
Answer: B
Question: 12, 38, 116, 350, 1052, ?
Options:
A)2158
B)3158
C)2178
D)4121
E)9186
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
Answer is B
Answer: B
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)Rs.10
B)Rs.2
C)Rs.5
D)Rs.3
E)Rs.4
Rationale: 1250 = D(100/4)2
D = 2
ANSWER:B
Answer: B
Question: John invests $x at the semi-annual constant compounded rate of 2 percent and also does $8,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
Options:
A)10000
B)12000
C)16160.8
D)14000
E)15000
Rationale: A = P(1+r/n)^nt
A= total amount accrued
P = principal deposited
r = rate of interest in decimal form
n = number of times per year, interest compounded
t = time in number of years.
.
x(1+0.02/2)^2 - x = 8,000(1+0.04/4)^4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)
=> x[(1.01)^2 - 1] = 8,000[(1.01)^4 - 1]
=> x[(1.01)^2 - 1] = 8,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides
=> x = 8,000(1.0201+1) =16160.8
Hence answer is C.
Answer: C
Question: How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even?
Options:
A)320
B)720
C)6480
D)2160
E)520
Rationale: let last digit is 2
when second last digit is 4 remaining 4 digits can be filled in 120 ways,similarly is second last digit is 6 remaind 4 digits can be filled in 120 ways,
so for last digit=2,total numbers=240
last digit=4,tot no=240
and last =6,tot no=240
so total of 720 even numbers are possible
ANSWER:B
Answer: B
Question: If 8 is added to twice a number and this sum is multiplied by 4, the result is the same as if the number is multiplied by 4 and 8 is added to the product. What is the number?
Options:
A)-6
B)-8
C)-9
D)10
E)11
Rationale: let the number be x;
4(8+2x)=4x+8;
x=-6
ANSWER:A
Answer: A
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)Rs. 650
B)Rs. 690
C)Rs. 698
D)Rs. 700
E)Rs. 712
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: C
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Irin bake?
Options:
A)0.125%
B)1.25%
C)55.4%
D)125%
E)0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, Irin baked 9*9.18 cookies or 82 cookies (approx)
% share = 82/148 = 55.4 approx
Hence, answer is C.
Answer: C
Question: According to a survey, at least 48% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
Options:
A)0%
B)3%
C)8%
D)15%
E)18%
Rationale: To minimize the percentage who like all three, let's maximize the percentage who like 2 out of 3.
80% like cherries and 20% don't like cherries.
Let's combine this with the people who like bananas.
20% don't like cherries but do like bananas.
55% like cherries and bananas.
25% like cherries but not bananas.
Now let's distribute the people who like apples.
20% like bananas and apples, but not cherries.
25% like cherries and apples, but not bananas.
3% like all three.
52% like cherries and bananas, but not apples.
The answer is B.
Answer: B
Question: If x + 4y = 5 and 5x + 6y = 7, then 3x + 5y = ?
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: Add the left terms and right terms of the two equation to obtain a new equation
x + 5x + 4y + 6y = 5 + 7
Group and simplify
6x + 10y = 12
Divide all terms of the above equation by 2 to obtain a new equation
3x + 5y = 6
correct answer A
Answer: A
Question: At what rate of interest is an amount doubled in two years, when compounded annually?
Options:
A)41.4%
B)43.4%
C)31.4%
D)30%
E)21.4%
Rationale: Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4%
ANSWER:A
Answer: A
Question: Which of the following is greatest?
Options:
A)2/3
B)6/3
C)7/3
D)8/3
E)10/3
Rationale: simply we know that 10/3 is greater than all others.
Answer is : E
Answer: E
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
Options:
A)776
B)744
C)299
D)257
E)125
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
Answer:B
Answer: B
Question: If b is greater than 1 , which of the following must be negative?
Options:
A)(2 - b)(b - 1)
B)(b - 1)/3b
C)(1 - b)^2
D)(2 - b)/(1 - b)
E)(1 - b^2)/b
Rationale: To be -ive, we should remember it should not be zero apart from being positive...
C will always be 0 or positive..
A and D will be zero at b=2..
B will always be positive..
left is E, where the numerator will always be negative and denominator, a positive..
ans E
Answer: E
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
Options:
A)1/7
B)3/7
C)2/7
D)6/7
E)5/7
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
ANSWER A
Answer: A
Question: Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 3 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?
Options:
A)2y
B)4y
C)5y
D)6y
E)25/3y
Rationale: Anthony performed for 14 days meansw Cindy performed for(14-3)=11 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/11
Solving we get, x=25/3y
Now Anthony's Advance is x=25/3y .So answer should be E.
Answer: E
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 8 kmph, then the speed of the boat in still water is :
Options:
A)2.5 km/hr
B)4.2 km/hr
C)5 km/hr
D)10.5 km/hr
E)None of these
Rationale: Solution
Speed of stream = 1/2 (18-8) km/hr=5kmph . Answer C
Answer: C
Question: A man bought 10 crates of mangoes for $160 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 25 percent of the total cost?
Options:
A)$35
B)$25
C)$45
D)$50
E)$55
Rationale: As given, after lost, the remaining 8 crates total cost = $160
So, 1 crate cost = 160/8 = 20
To get 25% profit, 1 crate cost should be = 20+20*25/100 =$25
Answer : B
Answer: B
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 8 days more?
Options:
A)1122
B)1140
C)1199
D)1188
E)1166
Rationale: 760 ---- 22
760 ---- 20
x ----- 8
x*8 = 760*20
x = 1900
760
-------
1140
Answer: B
Answer: B
Question: By weight, liquid X makes up 0.5 percent of solution P and 1.5 percent of solution Q. If 200 grams of solution P are mixed with 800 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution?
Options:
A)1.3%
B)1.2%
C)1.1%
D)1.0%
E)0.9%
Rationale: The number of grams of liquid X is 0.5(200)/100 + 1.5(800)/100 = 1 + 12 = 13 grams.
13 / 1000 = 1.3%
The answer is A.
Answer: A
Question: In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides?
Options:
A)1, 2, 5
B)3, 4, 5
C)4, 5, 6
D)7, 8, 9
E)5, 2, 4
Rationale: XY=3
YZ=1+XY = 4
XZ=1+YZ=5
B is the correct option.
Answer: B
Question: How many Z ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
Options:
A)3
B)16
C)28
D)32
E)56
Rationale: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen Z= 56 - 24 = 32
Ans: D
Answer: D
Question: The average of 25 results is 50. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?
Options:
A)741
B)752
C)878
D)785
E)458
Rationale: Solution: Sum of 1st 12 results = 12*14
Sum of last 12 results = 12*17
13th result = x (let)
Now,
12*14+12*17+x = 25*50
Or, x = 878.
Answer: Option C
Answer: C
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is ?
Options:
A)33.3
B)36.5
C)26.5
D)16.5
E)86.5
Rationale: Correct Sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = = 1825/50 = 36.5
Answer: B
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
A)33/91
B)33/18
C)33/29
D)33/18
E)33/12
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= 12C4/15C4
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer:A
Answer: A
Question: If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
Options:
A)89 days
B)90 days
C)85 days
D)99 days
E)79 days
Rationale: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (9*6*88/1) = (6*8*d/1)
on solving, d = 99 days.
Answer : D.
Answer: D
Question: At 15:00 there were 21 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?
Options:
A)7
B)14
C)25
D)27
E)30
Rationale: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 27
D
Answer: D
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
Options:
A)Rs.3750
B)Rs.3000
C)Rs.3200
D)Rs.2160
E)Rs.2000
Rationale: Explanation:
60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
ANSWER IS B
Answer: B
Question: There are 3 numbers x,y,z.the mean is m.median is 5.m is 10 more than the smallest number and 15 less than the biggest number.what is x+y+z?
Options:
A)20
B)30
C)35
D)40
E)45
Rationale: m=x+y+z/3
x+y+z=3m
median is middle number let y=5
let x is biggest number then x=m+15
z will be the smallest number then z=m-10
m+15+5+m-10=3m
m=10
then x+y+z=30
ANSWER:B
Answer: B
Question: whats the next no..
3,7,13,19....
Options:
A)27
B)28
C)29
D)30
E)31
Rationale: prime no.s from 3 onwards
3,5,7,11,13,17,19,23,29
write alternate primes no.s starting from 3
3,7,13,19,29
ANSWER:C
Answer: C
Question: Nine children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
Options:
A)240
B)480
C)540
D)720
E)840
Rationale: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 6!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 4 can sit in 5! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 6!-2*5!=840..
ans E
Answer: E
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Options:
A)299m
B)287m
C)279m
D)100m
E)277m
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: D
Question: If the roots of the equation 2x2 - 5x + b = 0 are in the ratio of 2:3, then find the value of b?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let the roots of the equation 2a and 3a respectively.
2a + 3a = 5a = -(- 5/2) = 5/2 => a = 1/2
Product of the roots: 6a2 = b/2 => b = 12a2
a = 1/2, b = 3.
ANSWER:A
Answer: A