divelab/Sys2Bench huggingface dataset:
Question: What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3?
Options:
A)1.4
B)sqrt (2)
C)1.7
D)sqrt (3)
E)2.0
Rationale: (A) 1.4
eqn of circle = x^2 + y^2 = 1, center = (0,0) radius = 1
min dist of line from circle = dist of line from the center - radius
Make the distance of the line from the circle to be 0 and we see that it becomes a tangent to the circle.
Now we know if we draw a line from the center to the point where the tangent touches the circle the line and the tangent are perpendicular to each other.
So we need to find the equation of this line first.
We can take the line back where it was now
Since the lines are perpendicular m1 x m2 = -1
m of line = 3/4
so slope of the new line = -4/3
Since the line passes through the origin (center of circle) its eqn => y=-4/3x
now we need to get the point of intersection of our two lines, which comes out to be (36/25,-48/25)
now get the distance of this point from the origin and subtract the radius from it.
Comes to 1.4 (may have made calculation errors )
So A.
Answer: A
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 1, 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 1, then the units digit of a+1 is either 1 or 9.
To satisfy both conditions, the units digit of a must be 8.
Then a+2 has the units digit of 0, thus the units digit of (a+2)^2 will be 0.
The answer is A.
Answer: A
Question: A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?
Options:
A)2/33
B)5/66
C)5/33
D)5/11
E)1/2
Rationale: No of Loose blue socks = 6 (3 pairs)
No. of Loose white Socks = 6 (3 pairs)
total no. of blue and white socks = 12
Total no. of socks to be selected = 4
So we have C (12,4) = no of ways the socks can be selected = 495
No of ways One pair of blue socks is selected ( 2 blue socks) , C (6,2) , No of ways one pair of white socks can be selected C (6,2) ..Because we have to find a scenario where EXACTLY one pair of Blue socks and ONE pair of WHITE socks is selected we will multiply the two .. ie 15 x 15 ..
Filling the information in the Probability formula we get P (A) = (15 x 15) / 495 = 5 /11
ANSWER : (D)
Answer: D
Question: The sum of the squares of three numbers is 241, while the sum of their products taken two at a time is 100. Their sum is:
Options:
A)20
B)11
C)21
D)41
E)None of these
Rationale: x^+y^2+z^2=241
xy+yz+zx=100
as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
so (x+y+z)^2=241+(2*100)
(x+y+z)^2=441
so x+y+z=21
ANSWER:C
Answer: C
Question: The average of ten numbers is 8. If each number is multiplied by 11, then what is the average of the new set of numbers?
Options:
A)8
B)11
C)19
D)88
E)121
Rationale: The sum of the ten numbers is 8*10 = 80
If each number is multiplied by 11, the new sum is 11*(80).
The average is then 11*8 = 88
The answer is D.
Answer: D
Question: What percentage of numbers from 1 to 100 have cube that end in the digit 5?
Options:
A)1
B)10.5
C)25
D)20
E)22
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 95 are 5,15,25,35,45,55,65,75,85,95.
Number of such numbers = 95.
Required percentage = (10/95 * 100) = 10.5%
ANSWER:B
Answer: B
Question: Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and U. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of U if J is negative?
Options:
A)-2
B)U=0
C)1
D)2
E)5
Rationale: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.
mode of the set is a number which occurs maximum number of time in the set. now, since U is the mode of the set. therefore U=0. hence answer is B
Answer: B
Question: If X, Y and Z are digits and 7XYZ is a 4-digit number that is divisible by 2, which of the following is a possible product of X, Y and Z?
Options:
A)17
B)42
C)13
D)27
E)51
Rationale: Key to this question is to remember the fact that a number divisible by 2 must end with 2 OR 0 (i.e Z).
If Z had to be 0, product should also be 0 regardless of X and Y.
The product is a multiple of 2. Only one answer choice meets the requirement.
Ans B.
Answer: B
Question: A sales executive gets 20% bonus of the total sales value and 10% commission besides the bonus on the net profit after charging such commission. If the total sales value be Rs. 10 lakh per annum and the total profit of the company be Rs. 1.32 lakh, then his total earning per annum will be, given that he is not entitled to receive any fixed salary from the company :
Options:
A)2.3 lakh
B)2.32 lakh
C)2.12 lakh
D)3.2 lakh
E)None of these
Rationale: Solution: His bonus,
= (20 *1000000) /100 = 2lakh
Total profit = net profit + (10 *net profit) /100
1.32lakh = net profit *[1 + (10/100)]
Net profit = 132000 /1.1 = 120000.
Commission,
= (total profit - net profit)
= 132000 - 120000
= 12000.
Hence, his total earnings = 2lakh + 12000 = Rs. 212000.
Answer: Option C
Answer: C
Question: If a Ã— b = 2a - 3b + ab, then 3 Ã— 2 + 2 Ã— 3 is equal to :
Options:
A)7
B)8
C)9
D)25
E)26
Rationale: Explanation:
3 Ã— 2 + 2 Ã— 3 = (2 Ã— 3 - 3 Ã— 2 + 2 Ã— 3) + ( 2 Ã— 2 - 3 Ã— 3 + 2 Ã— 3)
= (6 + 4 - 9 + 6) = 7.
Answer: A
Answer: A
Question: A sum of money deposited at compound interest (compounded yearly) amounts to $600 in 2 years and to $624 in 3 years. What is the interest rate?
Options:
A)2%
B)4%
C)6%
D)7%
E)8%
Rationale: 624 - 600 = 24
24/600 = 0.04 = 4%
The answer is B.
Answer: B
Question: In expressing a length 810472 km as nearly as possible with three significant digits , find the percentage error
Options:
A)0.34%
B)0.034%
C)0.0034%
D)0.00034%
E)3.4%
Rationale: Error = (81.5 – 81.472)km = 0.028.
Required percentage = [(0.028/81.472)*100]% = 0.034%.
Answer is B.
Answer: B
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 60 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)10 sec
B)16 sec
C)12 sec
D)67 sec
E)13 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 60 * 100/18 = 1000/3
RS = 60 + 40 = 100 * 5/18
T = 1000/3 * 18/500 = 12 sec
Answer: C
Answer: C
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Options:
A)33 1/8%
B)33 8/3%
C)33 1/3%
D)37 1/3%
E)33 1/4%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: C
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
Options:
A)2288
B)2667
C)2799
D)6725
E)2771
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer:D
Answer: D
Question: 6x − 12 = 6y
5y + 5x = 10
Which of the following is the number of solutions to the system of equations shown above?
Options:
A)More than three
B)Exactly three
C)Exactly two
D)Exactly four
E)None of these
Rationale: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
5y + 5x = 15
=>x + y = 2 -- 2
From equation 1 and 2 , we get
2x = 4
=> x=2
y=0
Therefore , the given system will have Exactly one solution
Answer : E
Answer: E
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 28% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
Options:
A)35.67%
B)64.75%
C)68.57%
D)70.20%
E)none of these
Rationale: Girls = 900, Boys = 1100
Passed = ( 28% of 1100 ) + ( 32% of 900)
= 308 + 288 = 596
Failed = 2000 - 596 = 1404
Failed % = [(1404/2000) x 100]%
= 70.2%.
ANSWER:D
Answer: D
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)21
B)28
C)90
D)100
E)11
Rationale: Explanation:
SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 5 = Rs. 100.
Answer: D
Answer: D
Question: 54671 - 10456 - 33466 = ?
Options:
A)2449
B)10449
C)10749
D)10449
E)6468
Rationale: C
If we calculate we will get 10749
Answer: C
Question: If |4x+6| = 42, what is the sum of all the possible values of x?
Options:
A)2
B)-3
C)4
D)-5
E)6
Rationale: There will be two cases
4x+6= 42 or 4x+6 = -42
=> x =9 or x= -12
sum of both the values will be -12 +9 = -3
Answer is B
Answer: B
Question: Find the value of m 62519 x 9999 = m?
Options:
A)724533811
B)625127481
C)545463251
D)725117481
E)677899932
Rationale: 62519 x 9999 = 62519 x (10000 - 1)
= 62519 x 10000 - 62519 x 1
= 625190000 - 62519
= 625127481
B
Answer: B
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
A)6
B)2
C)8
D)9
E)3
Rationale: Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 days. Answer: B
Answer: B
Question: Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What are their present ages?
Options:
A)16 and 40 years
B)13 and 37 years
C)10 and 34 years
D)11 and 35 years
E)20 and 44 years
Rationale: Let son's age 8 years ago be x years.
Then, Rohit's age 8 years ago = 4x years.
Son's age after 8 years = (x + 8) + 8 = (x + 16) years.
Rohit's age after 8 years = (4x + 8) + 8 = (4x+ 16) years.
2 (x + 16) = 4x + 16
2x = 16
x = 8.
Hence, son's 'present age = (x + 8) = 16 years.
Rohit's present age = (4x + 8) = 40 years.
Answer is A.
Answer: A
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Qâ€™s amount. At the end of the year 10% profit was earned which was equal to 98,000. What was the amount invested by R?
Options:
A)2,10,000
B)1,05,000
C)1,75,000
D)2,00,000
E)None of these
Rationale: Ratio for amount invested by P, Q & R
= 5x Ã— 12 : 6x Ã— 12 : 6x Ã— 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 10% of T
where, T = Total amount
T = 980000
Amount received by
R = 3x /3x+6x+5x(980000)
= 210000
Answer A
Answer: A
Question: A box has 210 coins of denominations one-rupee and fifty paise only. The ratio of their respective values is 13:11. The number of one-rupee coin is
Options:
A)65
B)66
C)77
D)78
E)NOne
Rationale: Solution: Respective ratio of the number of coins;
= 13:11*2 = 13:22
Hence, Number of 1 rupee coins;
= 13*210/(13+22) = 78.
Answer: Option D
Answer: D
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 18 miles, how many miles was Mike's ride?
Options:
A)30
B)34
C)38
D)42
E)48
Rationale: The cost of Annie's ride was 2.5+5+(0.25*18) = $12
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 12
0.25*x = 9.5
x = 38 miles
The answer is C.
Answer: C
Question: How many polynomials are there of the form x3rd - 8x2round + cx + d such
that c and d are real numbers and the three roots of the polynomial are
distinct positive integers?
Options:
A)0
B)1
C)1
D)2
E)5
Rationale: The sum of the roots of the polynomial is 8. Since the roots are distinct
positive integers, then they are either 1, 2, 5 or 1, 3, 4. Thus, the polynomial is either
(x − 1)(x − 2)(x − 5) or (x − 1)(x − 3)(x − 4).
correct answer C
Answer: C
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,051. How much did she invest at 5%?
Options:
A)$500
B)$600
C)$700
D)$900
E)$950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1051/1000)-1 = 0.051 = 5.1%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.051
(0.05)x +0.06 - (0.06)x = 0.051
-0.01x = -0.009
x= -0.009/-0.01 = 9/10 = 90%
So X = 90% of the 1000 which is 900
ANSWER:D
Answer: D
Question: 2, 1, (1/2), (1/4), ?
Options:
A)(1/3)
B)(1/8)
C)(2/8)
D)(1/16)
E)(3/16)
Rationale: This is a simple division series; each number is one-half of the previous number.
Answer : B.
Answer: B
Question: If x = (y)(y + 1) and y is a prime number less than 6, which of the following could not be the product of 2 consecutive integers?
Options:
A)a) 5x
B)b) 11x
C)c) 13x
D)d) 30x
E)e) 58x
Rationale: Given y is a prime number less than 6
possible values of y are 2 3 5
given, x=y*(y+1)
if y = 2 x=2*3=6
if y = 3 x=3*4=12
if y = 5 x=5*6=30
so possible values of x are 6,12,30
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 30x can be (30*31)
E. 58x cannot be
So answer option E
Answer: E
Question: Find for what value(s) of k would there be an unique solution for the given set of questions.
2x - 3y = 1 and kx + 5y = 7
Options:
A)-10/3
B)-10/9
C)-10/0
D)-10/1
E)-10/2
Rationale: : If two equations ax + by = M and cx + dy = N have a unique solution, then ac≠bdac≠bd
So in the above problem, k ≠−10/3
Answer:A
Answer: A
Question: 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
Options:
A)18
B)17
C)12
D)19
E)12
Rationale: 9M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days
Answer: C
Answer: C
Question: A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 11 years. What is the average age (in years) of the family?
Options:
A)26
B)28
C)30
D)32
E)34
Rationale: Total age of the grandparents = 66 Ã— 2 = 132
Total age of the parents = 40 Ã— 2 = 80
Total age of the grandchildren = 11 Ã— 4 = 44
Average age of the family = (132+80+44)/8 = 256/8 = 32 years
The answer is D.
Answer: D
Question: Shanmukham buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods
Options:
A)6999.2
B)6876.1
C)6654
D)7000
E)None of these
Rationale: Explanation :
Rebate = 6% of Rs. 6650 = Rs. 6/100 x 6650 = Rs. 399.
Sales tax = 10% of Rs. (6650 399) = Rs. 10/100 x 6251 = Rs. 625.10
Final amount = Rs. (6251 + 625.10) = Rs. 6876.10
Answer : B
Answer: B
Question: A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
Options:
A)Rs. 7.98
B)Rs. 8
C)Rs. 8.50
D)Rs. 9
E)Rs. 9.50
Rationale: petrol used in 1st yr = 4000/7.5 = 533.33 ltr
petrol used in 2nd yr = 4000/8 = 500 ltr
petrol used in 3 rd year = 4000/8.5= 470.59 ltr
Total petrol used for Rs.12000(4000/- for each yaer) in 3rd yrs = 1503.92 ltr
Average cost per litre = 12000/1503.92 = Rs 7.98
ANSWER:A
Answer: A
Question: Sum of the squares of three numbers is 129 and the sum of their products taken two at a time is 250. Find the sum?
Options:
A)20
B)23
C)25
D)26
E)29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 129 + 2* 250
a + b + c = √529 = 23
B
Answer: B
Question: Nitin borrowed 8000 at the rate of 6% p.a. for the first three years, 8% p.a.for the next five years and 12% p.a.for the period beyond eight years. At the end of eleven years how much money did he give as interest?
Options:
A)8000
B)10,000
C)5,000
D)7,520
E)None of these
Rationale: Let the interest be i Then,
(8000×3×6/100)+(8000×5×8/100)+(8000×3×12/100)=i
⇒ 1440 + 3200 + 2880 = i
⇒ i = 7520
Answer D
Answer: D
Question: In a group of 90 students, 36 are taking History, and 30 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?
Options:
A)9
B)19
C)23
D)27
E)29
Rationale: Number of students taking history =H=36
Number of students taking statistics =S= 30
Total number of students =T= 90
Number of students taking History or Statistics or both =B= 59
Number of students taking neither history nor statistics =N= 90-59=31
LetXbe the number of students taking both history and statistics.
Then
T = H + S + N - X
or 90 = 36 + 30 +31 - X
or X = 7
Now,
Number of students taking only history will be
H-X
or 36-7 = 29
Answer:- E
Answer: E
Question: If k and y are integers, and 10k + y is odd , which of the following must be true?
Options:
A)k is odd
B)k is even
C)y is odd integer
D)y is even
E)both k and y are odd
Rationale: 10k will be always even as 10 has 2 as one of its factors
if 10k+y is odd, then the only possible explanation is that y is odd
correct answer C
Answer: C
Question: Which of the following is equal to (y+1)!/y!?
Options:
A)y-1
B)1+(1/y)
C)1
D)y+1
E)y
Rationale: (y + 1)! = (y + 1) * x!
(y + 1)!/y! = y + 1
Answer: D
Answer: D
Question: A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minutes to deer’s 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it catches the deer ?
Options:
A)600m
B)700m
C)800m
D)1000m
E)1200m
Rationale: Tiger takes 5 leaps /m and Deer takes 4 leaps/ m
Thus, tiger runs at the speed of 5 x 8 = 40 m/min
and deer runs at the speed of 4 x 5 = 20 m/min
Tiger is 50 leaps behind,which is 50 x 8 = 400 m
Relative speed of tiger and deer is = 20 m/min
Thus, 400/20 = 20 m
Thus,the tiger will catch deer = 20 x 40 =800 m
ANSWER:C
Answer: C
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number
Options:
A)8
B)10
C)12
D)14
E)15
Rationale: Explanation:
=> 3(2x+9) = 75
=> 2x+9 = 25
=> x = 8
Answer: Option A
Answer: A
Question: An event manager has ten patterns of chairs and eight patterns of tables.In how many ways can he make a pair of table and chair?
Options:
A)70
B)60
C)100
D)80
E)90
Rationale: He has 10 patterns of chairs and 8 patterns of tables.
Hence,A chair can be arranged in 10 ways
A table can be arranged in 8 ways
Hence one chair and one table can be arranged=(10*8)ways
=80 ways
Answer is option D
Answer: D
Question: If there are 4 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
Options:
A)32
B)24
C)56
D)44
E)40
Rationale: The first member can be anybody, so 8 possibilities.
The second member cannot be the sibling of the previous member, therefore 6 possibilities (anybody from the remaining 3 pairs).
Finally, the third member, can be chosen from the remaining 2 pairs, so 4 possibilities.
This would give us 8*6*4 possibilities, but in this case we don't care about the order in which we choose them, we have to divide the product we obtained by 6(=3!), which is the number of possibilities we can chose the same three distinct members, say ABC (it can be BAC, CAB,...). You can count those possibilities for such a small number as 3, but why avoid permutations? Is it better to start listing the possibilities instead of just accepting the already proven result?
So, the correct answer is 8*4=32.
Answer A.
Answer: A
Question: Two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km/hr and 36 km/hr. The time of crossing each other, if they run in the opposite direction is
Options:
A)322 sec
B)14 sec
C)11sec
D)13 sec
E)34 sec
Rationale: Explanation:
Total distance to be covered = 156.62 + 100 = 256.62 m
Trains are running in opposite directions, hence
Relative speed = 30 + 36 = 66 km/hr = 18.33 m/sec
Time = Distance / Relative Speed
= 256.62 /18.33 sec
= 14 sec
Therefore, the time of crossing each other in the opposite direction is 14 seconds.
ANSWER: B
Answer: B
Question: James can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
Options:
A)40 minutes.
B)1 hour and 30 minutes.
C)1 hour
D)1 hour and 40 minutes.
E)2 hours and 15 minutes
Rationale: Rate =Output/Time
James Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
Combined Rate*Combined Time= Combined Output
20/12*t=150
t=90 mins => 1 hr 30 min
ANSWER:B
Answer: B
Question: The mean proportional between 234 and 104 is
Options:
A)12
B)39
C)54
D)156
E)None
Rationale: Sol.
Required mean proportional = √234 x 104
= √13x9x2x13x8 = (13x3x4) = 156.
Answer D
Answer: D
Question: How many positive integers will divide evenly into 560?
Options:
A)8
B)12
C)16
D)18
E)20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 20
Option E
Answer: E
Question: George takes 30 days to do a piece of work and Mark takes 45 days for the same work. For the first 15 days only George works. Then Mark also joins him. Find the time taken to complete the entire work.
Options:
A)24 days
B)25 days
C)26 days
D)27 days
E)28 days
Rationale: George 1 day work= 1/30
Mark 1 day work= 1/45
George 15 day work= 15*1/30 =1/2
Work remaining= 1-1/2 =1/2
George + Mark 1 day work= 1/30 + 1/45 =1/18
Number of day required to complete 1/2 work= (1/2)/(1/18)= 9 days
So total days required to complete the work is 15+9= 24 days.
ANSWER:A
Answer: A
Question: What is the probability of rolling a total of 5 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
Options:
A)1/12
B)1/6
C)2/7
D)1/3
E)1/9
Rationale: Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 5 i.e. (1+4), (2+3), (3+2), (4+1)
So, total probability is 4/36 or 1/9.
Answer is E.
Answer: E
Question: The number of meters in WB is equal to the square root of the number of centimeters in WB. What is the length of WB (1 meter=100 centimeters)?
Options:
A)100 meters
B)10 meters
C)100 centimeters
D)10 centimeter
E)1 centimeter
Rationale: I'd plug in the options for this question.
Check option A: if the number of meters in WB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.
Answer: A.
Answer: A
Question: (17)3.75 x (17)? = 178
Options:
A)2.29
B)2.75
C)4.25
D)4.5
E)None of these
Rationale: Solution
let (17)3.75 * (17)x = 178. then, (17)3.5 + x = (17)8.
∴ 3.75 + x = 8 ⇔ x = (8 - 3.75) ⇔ x = 4.25
Answer C
Answer: C
Question: There are 10 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?
Options:
A)15
B)16
C)28
D)56
E)90
Rationale: Every team plays with 9 teams...so total no of matches = 10 x 9 = 90.
Now, each match is played twice => 90 x 2
But 2 teams play a match => 90 x 2 /2 = 90.
Answer: E
Answer: E
Question: Four of the following five are alike in a certain way and hence form a group. Which one does not belong to the group?
Options:
A)70
B)80
C)52
D)48
E)68
Rationale: A
All the numbers are multiple of 4, except 70.
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 26 years now, the son's age five years back was?
Options:
A)8 years
B)14 years
C)18 years
D)19 years
E)15 years
Rationale: Let the son's present age be x years.
Then, (26 - x) = x
2x = 26 => x = 13
Son's age 5 years back = (13 - 5)
= 8 years.
Answer: A
Answer: A