divelab/Sys2Bench huggingface dataset:
Question: Townville has 100 residents, and 20 of them are females. If half of Townville’s male residents are smokers, and 1/2 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: Number of people =100
Females = 20
men = 100-20=80
Half of the men are smoker80/2=40, that means the remaining men 80-40=40 are non smokers.
1/2 females are smoker. i.e 1/2*20 = 10
20-10=10 females are non smokers
So, total number of non smokers in the town are 40+10 =50
Answer : C
Answer: C
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)12 sec
B)24 sec
C)48 sec
D)60 sec
E)62 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
ANSWER:C
Answer: C
Question: A jeep takes 3 hours to cover a distance of 440 Km. how much should the speed in Kmph be maintained to cover the same direction in 1/2th of the previous time?
Options:
A)48 Kmph
B)252 Kmph
C)293 Kmph
D)263 Kmph
E)265 Kmph
Rationale: Time = 3
Distance = 340
1/2 of 3 hours = 6 * 1/2 = 1.5 Hours
Required speed = 440/1.5 = 293 Kmph
C)
Answer: C
Question: There are 3 people A,B & C. Rs.700 is divided among A,B & C so that A receives 1/2 as much as B and B 1/2 as much as C. What is the C's share is?
Options:
A)Rs.100
B)Rs.200
C)Rs.400
D)Rs.500
E)Rs.550
Rationale: Let C's share = Rs.x. Then
B's share = Rs.x2
And, A's share = Rs.x4
A:B:C = x4:x2:x=1:2:4
Hence, C's share = Rs.(700×47) = Rs.400
C
Answer: C
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 17% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
Options:
A)5%
B)13%
C)21%
D)11%
E)30%
Rationale: 60-(x+17+z) + 50-(x+17+y) + 35-(z+17+y) + x + y + z +17 = 100
where x = people who bought MilkChicken
y = people who bought chickenApples
z= people who bought Milk and Apples
x+y+z= the number of people who bought just exactly two products.
Hence solving the above equation we get,
111 -(x+y+z) = 100
Thus, x+y+z= 11
Answer: D
Answer: D
Question: A cricket bat is sold for $900, making a profit of $225. The profit percentage would be
Options:
A)24%
B)25.5%
C)33.33%
D)36.3%
E)40%
Rationale: 225/(900 - 225) = 33.33%.
Answer: C
Answer: C
Question: BILAL spends 30% of his salary on house rent and 55% of the remaining money on food and clothes. He saves the remaining amount. If he saves ?59724 yearly, how much amount does he spend on food and clothes per month ?
Options:
A)5316
B)4792
C)5817
D)6080
E)6083
Rationale: Let his monthly salary be y.
House rent expenditure = 30/100 y = 3y/10
âˆ´ Remaining = 7y/10
Expense of food = 7y/10 x 55/100 = 77y/200
âˆ´ Remaining = 7y/10 - 77y/200
= 140y - 77y/200 = 63y/200
Monthly saving = 59724/12 = 4977
âˆ´ 63y/200 = 4977 = y= 4977 x 200/63 = 15800
Expenditure on food and clothes = 77y/200
= 6083
Answer: E
Question: The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree is
Options:
A)30°
B)45°
C)60°
D)90°
E)None
Rationale: Solution
Let AB be the tree and AC be its shadow.
Then, < ABC	= θ.
Then, AC/AB	= √3
cotθ= √3
θ=30°
Answer A
Answer: A
Question: If the two-digit integers K and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of K and N?
Options:
A)181
B)165
C)121
D)99
E)44
Rationale: Since the question asks for the answer that CANNOT be the sum of K and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that K and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of K and N.
Let's start with the 'easiest' answer first:
44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E
Now let's work through the rest of the list....
Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D
Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C
Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B
There's only one answer left....
A
Answer: A
Question: For any real number x, the operatoris defined as:
(x) = x(3 − x)
If p + 1 =(p + 1), then p =
Options:
A)−3
B)0
C)1
D)2
E)3
Rationale: (x) = x(1 − x)
(p + 1) = (p + 1)(3 - p - 1) =(2 -p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (2-p)(p+1) = (p + 1)
Or (p + 1) + (p-2)(p+1) = 0
(p + 1)(p-2) = 0
p = -1,p=2
Option D
Answer: D
Question: In how many different number of ways 5 boys and 2 girls can sit on a shopa which can accommodate persons?
Options:
A)180
B)190
C)200
D)210
E)None
Rationale: Option 'D'
7p3 = 7 × 6 × 5 = 210
Answer: D
Question: A train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 98 miles per hour, what is the value of y?
Options:
A) 68
B) 84
C) 90
D) 120
E) 125
Rationale: Average speed=Total distance traveled /Total time taken
3d/d/60+d/y+d/160=98
Solving for d and y,
15y=11y+480
4y=500
y=125
Answer E
Answer: E
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 9 minutes, then the area of the park (in sq. m) is:
Options:
A)153601
B)153600
C)153602
D)153603
E)194400
Rationale: Perimeter = Distance covered in 9 min. =(12000/60) x 9m = 1800 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1800 or x = 180.
Length = 540 m and Breadth = 360 m.
Area = (540 x 360) m2 = 194400 m2.
Answer: E
Answer: E
Question: Of the 8 members of teacher in school, 5 can teach Physics, 7 can teach Math, and 4 can teach both subject. If one member is chosen at random, what is the probability that the member chosen will be someone who can not teach either subject?
Options:
A)a) 5/18
B)b) 7/18
C)c) 1/2
D)d) 0
E)e) 13/18
Rationale: You know how to solve for Total number of people who can teach at least one subject:
Total = n(A) + n(B) - n(A and B)
Total people who can teach at least one subject = 5 + 7- 4 = 8
So 8 people know how to teach at least one subject. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to teach any subject.
Answer (D)
Answer: D
Question: In a certain Parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle?
Options:
A)55
B)80
C)85
D)90
E)95
Rationale: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).
Given: x+(x+70)=180 --> x=55.
Answer: A.
Answer: A
Question: A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
Options:
A)37
B)299
C)72
D)Rs 32
E)01
Rationale: Explanation:
Let cost price of lemons be x.
Selling price of lemons becomes CP - loss.
=>SP= x-(20/100)x
=>40=x(80/100)
=>50
So 45 lemons cost Rs 50
Cost of 1 lemon = 50/45 Rs
Cost of 24 lemons = (50/45)*24 =80/3 Rs
Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32
ANSWER:D
Answer: D
Question: If M = 775 × 778 × 781, what is the remainder when M is divided by 14?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: M 775/14 leaves a remainder 5
778/14 leaves a remainder 8
781/14 leaves a remainder 11
5*8*11 =440
So the remainder will be the remainder of 440/14 which is 6
Ans A
Answer: A
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
Options:
A)15 hrs
B)20 hrs
C)25 hrs
D)30 hrs
E)10 hrs
Rationale: first pipe = x
ssecond and third (x-5)and (x-9)
1/x+1/(x-5)=1/(x-9)=>X=15
ANSWER A
Answer: A
Question: 6 women can do 75 units of work in 8 days by working 5hrs/day. In how many days can 4 women do 30 units of work by working 8hrs/day ?
Options:
A)3days
B)4days
C)5days
D)6days
E)7days
Rationale: 6x8x5/75=4x8xA/30
solve this for A then we get A=3days
ANSWER:A
Answer: A
Question: If a - b = 3 and a^2 + b^2 = 29, find the value of ab.
Options:
A)12
B)15
C)10
D)18
E)13
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 29 - 9 = 20
ab = 10.
Answer is C.
Answer: C
Question: 1,257
1,275
1,527
........
........
+7,521
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,5 and 7 exactly once in each integer. What is the sum W of the 24 integers ?
Options:
A) 26,996
B) 44,406
C) 60,444
D) 66,660
E) 99,990
Rationale: This is the way i solved it :
Total no. of different combos = 24, total digits 4 therefore each digit must repeat 24/4 = 6 times in each row .. So the right most row would add up to 1x6 + 2x6 + 5x6 + 7x6 = 6+12+30+42 = 90 .. Each row would add up to 90, so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90+9 and 9 stays and one 9 goes to the row to the left, so the last two digits of the SUM W should be 90 (E) .. We could go on and solve the exact number but since only one answer choice has the last digits as 90 we needn't go any further..
Answer: E
Question: In an exam, C scored 35 percent, D scored 65 percent and E 50 percent. The maximum score awarded in the exam is 2000. Find the average mark scored by all the three candidates?
Options:
A)100
B)500
C)1000
D)1500
E)2000
Rationale: Average mark scored by all the three boys
= [35/100 (2000) + 65/100 (2000) + 50/100 (2000)] / 3
= 1000
Answer: C
Answer: C
Question: On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:
Options:
A)47619
B)49619
C)47719
D)57619
E)47611
Rationale: Last digit should be 9.
when multiplying 7 with 9 , we get 63.
place 3 at unit place , we get 6 as carry.
Next digit of number should be such that we get product with 7 as a number whose last digit is 13-6=7.
such number is 1.
when 7 is multiplied with 1 , we get 7.
add carry 6 to it and we get 13.
so 3 will get at tens place and 1 carry for next place.
so next digit should give last digit as 2 (3-1=2).
such digit is 6.
...
..
so continuing like this , we get desired number as 47619
ANSWER:A
Answer: A
Question: What is the sum of the odd integers from 55 to 65, inclusive?
Options:
A)495
B)360
C)555
D)600
E)605
Rationale: The mean is 60.
Sum=Mean(# of elements)
There are 6 odd numbers between 55-65 inclusive. 6*60=360
B
Answer: B
Question: If x = -5 and y = 8, what is the value of 2(x-y)^2 - xy ?
Options:
A)358
B)348
C)368
D)388
E)378
Rationale: x = -5 and y = 8
x-y = -5 - 8 = -13
x*y = -5 * 8 = -40
Now we apply it in the equation 2(x-y)^2 - xy =2(-13)^2-(-40)
==>2*169 +40 = 338+40 =378
Answer : E
Answer: E
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 11 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options:
A)6.24
B)7.4
C)7.92
D)6.28
E)7.24
Rationale: Net part filled in 1 hour = (1/4 - 1/11) = 7/44
The cistern will be filled in 44/7 hrs i.e., 6.28 hrs.Answer: D
Answer: D
Question: If Mason is now twice as old as Gunther was 10 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now?
Options:
A)4G-8
B)3G
C)2G-8
D)AG-8
E)5F-2
Rationale: G is Gunther's current age.
Let Mason's current age be M.
given M = 2(G-10).
four years from now Mason's age will be = 2(G-10) + 10 = 2G-10
four years from now Gunther's age will be = G+10
Sum of ages of Mason and Gunther's after 4 years = 2G-10+G+10 = 3G
Ans : B
Answer: B
Question: A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room?
Options:
A)110
B)124
C)96
D)117
E)127
Rationale: Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117
ANSWER:D
Answer: D
Question: If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?
Options:
A)25%
B)30%
C)50%
D)70%
E)80%
Rationale: (Explanation:Friends, we know we will need gain amount to get gain percent, right.
So lets get gain first.
Let the cost price of 1 pen is Re 1 Cost of 8 pens = Rs 8 Selling price of 8 pens = 12
Gain = 12 - 8 = 4 Gain%=(GainCost*100)%=(48*100)%=50%
C
Answer: C
Question: If a: b :: 3 : 7, then what is (5a+6b): (a-3b)?
Options:
A)-57:2
B)-57:11
C)11 : 10
D)-11 : 10
E)-1 : 10
Rationale: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-3]= [5*(3/7)+6]/[(3/7)-3]= -57/2
ANSWER:A
Answer: A
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
Options:
A)15 kmph
B)8 kmph
C)9 kmph
D)1 kmph
E)2 kmph
Rationale: Explanation:
Distance=Speed*Time
90 * 10/60 = 15 kmph
ANSWER:A
Answer: A
Question: There are 690 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
Options:
A)75
B)100
C)115
D)175
E)225
Rationale: female = x
Male = 690-x
x/2 + 690-x/4 = 1/3* (690)= 230
x= 230
x/2 = 115 is supposed to be the answer
M is missing something
Correct Option C
Answer: C
Question: If the price of a computer were reduced by 11 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
Options:
A)$844.10
B)$895.20
C)$1,055.20
D)$1,135.20
E)$1,262.40
Rationale: Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-11/100)------->X(8/9)=A(say)
means X=A*(9/8).....
so initial price to be integer(As per stem) final price must be multiple of 8
if we check options all were divisible by 8 except option (A)..which is Ans.
Ans A
Answer: A
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
Options:
A)30, 40
B)30, 46
C)30, 49
D)30, 43
E)30, 43
Rationale: Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40..Answer:A
Answer: A
Question: Two cars cover the same distance at the speed of 62 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Options:
A)1873
B)1848
C)1984
D)1838
E)1939
Rationale: Explanation:
62(x + 1) = 64x
X = 31
62 * 32 = 1984 km
Answer: Option C
Answer: C
Question: In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Options:
A)21
B)22
C)28
D)25
E)30
Rationale: A:B = 100:75
B:C=100:96
A:C = 100/72 = 100:72
A beats(100-72) = 28 m
ANSWER C
Answer: C
Question: Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 6 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 6 younger brothers to get an equal number of cards?
Options:
A)110
B)112
C)116
D)118
E)120
Rationale: This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/6)*(x/2) is an integer
Or x/12 is an integer.
Hence we need the lowest multiple of 12 from the given options.
Let us start from the lowest value:
Option A: 110. This is not a multiple of 12
Option E: 120 = 12*10. This is a multiple of 12. Hence the correct answer.
Correct Option: E
Answer: E
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
Options:
A)9
B)3
C)2
D)4
E)5
Rationale: x/2 â€“ x/3 = 6 => x =6
3 + 6 = 9
Answer A
Answer: A
Question: In what ratio must rice at $9.30/kg be mixed with rice at $10.80/kg so that the mixture is worth $10/kg?
Options:
A)1:3
B)9:4
C)8:7
D)11:9
E)11:7
Rationale: 9.30x + 10.80y= 10(x+y)
.80y= .70x
x/y= 8/7
C is the answer
Answer: C
Question: What is the difference between local value & face value of 9 in the numeral 65693?
Options:
A)84
B)89
C)81
D)90
E)10000
Rationale: (Local value of 9) - (Face value of 9)
= (90 - 9) =81
C
Answer: C
Question: Anand finishes a work in 7 days, Bittu finishes the same job in 8 days and Chandu in 6 days. They take turns to finish the work. Anand on the first day, Bittu on the second and Chandu on the third day and then Anand again and so on. On which day will the work get over?
Options:
A)3rd
B)6th
C)9th
D)7th
E)8th
Rationale: They completed 146/168 work in 6 days working one by one on eacg day.
On 7 th day , 22/168 work is left which will be completed by Anand on 7th day.
ANSWER:D
Answer: D
Question: What is the sum of all the multiples of 12 between 30 and 200?
Options:
A)1648
B)1632
C)1626
D)1612
E)1800
Rationale: You first have to know all the multiples of 12 between 30 and 200. They are 12,24,36,48,60,72,84,96,108,120,132,144,156,168,180192. If you add all these numbers together, you get 1632.
Final Answer:
B
Answer: B
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 50 m long and 16 1/2 m board?
Options:
A)99
B)18
C)165
D)10
E)15
Rationale: 50 * 33/2 = 5/2 * 2 * x => x
= 165
Answer:C
Answer: C
Question: 4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are
Options:
A)4
B)8
C)12
D)16
E)None of these
Rationale: Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.
Answer C
Answer: C
Question: If 3x - y = 6 and x+2y = 8, then what is the value of 4x + y?
Options:
A)1/7
B)14
C)15
D)52/7
E)60/7
Rationale: 3x-y=6 ...equation 1
x+2y=8 ...equation 2
adding both the equations
4x+y=14
correct answer option B
Answer: B
Question: A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 21 adults have their meal, find the total number of children that can be catered with the remaining food.
Options:
A)33
B)54
C)63
D)17
E)01
Rationale: Explanation:
As there is meal for 70 adults and 21 have their meal, the meal left can be catered to 49 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 49 adults = 63 children
Hence, the meal can be catered to 63 children.
ANSWER: C
Answer: C
Question: If the number of 37,29n, where n represents the ones digit, is a multiple of 3, then the value of n could be which of the following?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.
i.e 3+7+2+9+n = multiple of three
or, 21 + n = multiple of 3.
If n=3, 21 + n =24,which is a multiple of 3.
Hence answer is C.
Answer: C
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years.
Options:
A)1:2
B)2:1
C)2:2
D)2:3
E)None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗6/100) /(P∗R∗9/100)]
=6PR /9PR=2:3
Option D
Answer: D
Question: Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
Options:
A)12
B)21
C)27
D)35
E)36
Rationale: For every 2 history books, there are 7 fantasy books:
Originally H:F = 2:7 = 6:21.
For every 3 fantasy books, there are 8 reference books:
F:R = 3:8 = 21:56
H:F:R = 6:21:56
After the changes, H:F:R = 12:21:56
There are fewer than 60 fantasy books, so there are 21 or 42 fantasy books.
The number of history books could be 12 or 24.
The answer is A.
Answer: A
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)267
B)280
C)279
D)177
E)288
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Answer: B
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 300 revolutions. How many revolutions does the second wheel make in covering d feet?
Options:
A)300xy
B)300x/y
C)300x - y
D)200y/x
E)600x/y
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
300 = d/(x*pi)
d = 300 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (300 * x * pi) / (y*pi) = 300x/y
Answer (B)
Answer: B
Question: Find the average of all prime numbers between 10 and 40
Options:
A)15.6
B)22.5
C)18.6
D)32.2
E)26.9
Rationale: Prime numbers between 10 and 40 are 11, 13, 17, 19, 23, 29, 31, 37
Required average = (11+ 13+ 17+ 19+ 23+ 29+ 31+ 37)/8 = 180/8 = 22.5
Answer is B
Answer: B
Question: If Log2 x - 5 Log x + 6 = 0, then what would the value / values of x be?
Options:
A)5.3296
B)6.3296
C)7.3296
D)8.3296
E)9.3296
Rationale: log(2x)-5log(x)+6=0 (given)
log(2x)-log(x^5)=-6
log(2x/x^5)=-6 [since log(a)-log(b)=log(a/b)]
apply anti log
2/(x^4)=e^-6
2/(x^4)=2.4788*10^-3
x^4=806.85
x=5.3296
ANSWER:A
Answer: A
Question: How many positive integers less than 10,000 are such that the product of their digits is 30?
Options:
A)12
B)24
C)36
D)38
E)50
Rationale: 30 = 1 * 30, 2 * 15, 3* 10, 5 *6
We have the option of using single digits 1,2,3,5 and 6
No : of four digit numbers such that the product is 30
The possible combinations are using digits (1,2,3,5) & (1,1, 5, 6) such that the product 30.
No: of different combinations possible using (1,2,3,5) = 4! = 24
No: of different combinations possible using (5,6,1,1) = 4!/2! = 12 ('1' is repeated twice)
Total 4 digit numbers so that the product is 30 is 24+12 = 36
No: of three digit numbers such that the product is 30
The possible combinations are using digits (2,3, 5) & (1,5,6)
No: of different combinations possible using (2,3,5) = 3! = 6
No: of different combinations possible using (1,5,6) = 3! = 6
Total 3 digit numbers so that the product is 30 is 6+6 = 12
No: of 2 digit numbers such that the product is 30 is 2 (56 and 65)
Total numbers under 10000 such that the product is 30 is 36+12+2 = 50
E
Answer: E
Question: Dawson has to secure 30% marks to clear his exam of class 8th.
He got 30 marks and failed by 36 marks.
What is the maximum marks ?
Options:
A)180
B)190
C)200
D)210
E)220
Rationale: E
220
To pass the exam ravish needs 30 + 36 = 66 marks.
=> (66/30) *100 = 220
Answer: E
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
A)226
B)992 rs
C)665
D)771
E)211
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
Answer: B
Answer: B