mathewhe/aqua_rat huggingface dataset:
Question: The ratio of male to female in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by half of the males and half of the females in the class?
(A) a)180 degree
(B) b) 168 degree
(C) c)191 degree
(D) d)192 degree
(E) e)204 degree
Rationale: let the common ratio be x.. so M=2x and F=3x and Total=5x
1/2 of M= 2x/2 and 1/2 of F= 3x./2.
Total preferring that carrer =x+3x/2=5x/2..
Now 5x= 360, so x=360/5=72..
so 72*5/2=180
A
Answer: (A) a)180 degree
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 120 envelopes
(A) 2 minutes
(B) 5 minutes
(C) 7 minutes
(D) 3 minutes
(E) 4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envelopes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 120 envelopes they will take 120/60 mins. i.e., 2 mins.
ANSWER:A
Answer: (A) 2 minutes
Question: 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 40 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
(A) 1
(B) 9/14
(C) 2/3
(D) 7/8
(E) 8/7
Rationale: Say total male = 40
Total female =60
Required ratio =( .4/40)/ (.6/60) = 1 A is the answer
Answer: (A) 1
Question: What will be the simple interest on Rs. 80,000 at 16(2/3) % per annum for 9 months?
(A) 8,000
(B) 9,000
(C) 10,000
(D) 11,000
(E) None of these
Rationale: Explanation:
Given:
1) Principal = Rs. 80,000
2) Rate of interest = 16(2/3)%
3) Time = 9 months
Rate of interest = 16(2/3)%=50/3
Time =	9/12=3/4 years
Simple Interest =	(P × R × T)/100
Substituting the given values, we get
Simple Interest =	80,000/100	×	50/3	×	3/4
Simple Interest = Rs.10,000
ANSWER IS C
Answer: (C) 10,000
Question: Pat, kate and mark charged a total of 216 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
(A) 18
(B) 36
(C) 120
(D) 90
(E) 108
Rationale: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 216 -total hours charged for,
x= 24.
Mat charged 6x-x or 5x for more hours than kate, or for 120 hours .
C is correct
Answer: (C) 120
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 30% on the cost price?
(A) 62.5
(B) 62.3
(C) 65
(D) 62.2
(E) 62.9
Rationale: CP = 47.50
SP = 47.50*(130/100)
= 61.75
MP*(95/100)
= 61.75
MP = 65
Answer:C
Answer: (C) 65
Question: If two numbers are in the ratio 1:2. If 10 is added to both of the numbers then the ratio becomes 2:3 then find the smallest number?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Explanation:
1:2
x + 10 : 2x + 10 = 2 : 3
3[x + 10] = 2[2x + 10]
3x + 30 = 4x + 20
9x - 8x = 40 - 30
x = 10
Then smallest number is = 1
1 * 10 = 10
Answer : A
Answer: (A) 10
Question: What is the least number of squares tiles required to pave the floor of a room 8 m 82 cm long and 2 m 52 cm broad?
(A) 14
(B) 20
(C) 40
(D) 44
(E) 48
Rationale: Length of largest tile = H.C.F. of 882 cm and 252 cm = 126 cm.
Area of each tile = (126 x 126) cm2.
Required number of tiles =882 x 252/(126^2)= 14.
ANSWER:A
Answer: (A) 14
Question: There are 5 girls and 5 boys. If they are to be seated in a row, what is the probability that no two girls sit together?
(A) A)1/10!
(B) B)2*5!5!/10!
(C) C)6!6!/10!
(D) D)6!6!/12!
(E) E)6!7!/12!
Rationale: If girls are alternate, then only no 2 girls can be together.
So among 10 places, girls can be seated in 5 alternate places in 5! ways.
And boys can be seated in the remaining 5 places in 5! ways.
Therefore total number of ways = 5! * 5!
But there could be 2 such arrangements-->
1. When first place is filled by a girl
2. When first place is filled by a boy
Therefore total number of ways = 2*5! * 5!
Also total number of ways to fill 10 places = 10!
Hence probability =2∗5!5!/10!
Answer:B
Answer: (B) B)2*5!5!/10!
Question: Sides of a triangle are 13 cm.14cm.and 15cm.respectively.calculate the area of triangle.
(A) 80
(B) 82
(C) 84
(D) 86
(E) 88
Rationale: let a=13cm, b=14cm.and c=15 cm.
s=1/2(13+14+15)=21,(s-a)=8,(s-b)=7 and (s-c)=6
Area=√21*8*7*6=84 sq.cm
Answer C
Answer: (C) 84
Question: Which of the following CANNOT yield an integer when divided by 7 ?
(A) The sum of three consecutive integers
(B) An integer with only even prime factors
(C) The product of two odd integers
(D) An integer divisible by 8
(E) An even integer
Rationale: An integer to be divisible by 7, must have 7 in its prime factorization. Thus an integer with only even prime factors (2^n) CANNOT be divisible by 7.
As for the other options:
(A) The sum of three consecutive integers --> if the three integers are {-1, 0, 1}, then their sum is 0 and 0 IS divisible by 7.
(C) The product of two odd integers --> 1*7=7 --> 7 is divisible by 7.
(D) An integer divisible by 8 --> 0 is divisible by both 7 and 8.
(E) An even integer --> 0=even is divisible by 7.
Answer: B.
Answer: (B) An integer with only even prime factors
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
(A) 22
(B) 33
(C) 55
(D) 4
(E) 9
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100 =
0.04 * 100 = 4%.Answer: D
Answer: (D) 4
Question: Virat buys an old car for Rs. 50000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 60000, his gain percent is:
(A) 11 (1/9) %
(B) 11 (1/8) %
(C) 11 (4/9) %
(D) 13 (1/9) %
(E) 51 (1/9) %
Rationale: Explanation:
C.P. = Rs. (50000 + 4000) = Rs. 54000
S.P. = Rs. 60000.
Gain% = ( (6000 / 54000) * 100 ) % = 11 (1/9)%
ANSWER: A
Answer: (A) 11 (1/9) %
Question: A train passes a station platform in 36 sec and a man standing on the platform in 22 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 288
(B) 210
(C) 881
(D) 1277
(E) 121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 22 = 330 m.
Let the length of the platform be x m . Then,
(x + 330)/36 = 15 => x = 210 m.
Answer: B
Answer: (B) 210
Question: The age of mother one decade age was three times the age of her daughter. 10 years hence, mother’s age will be two times that of her daughter. The proposition of their current ages is:
(A) 7:3
(B) 6:3
(C) 8:3
(D) 2:3
(E) 6:3
Rationale: A
7:3
Let, Ages of mother and daughter 1 decade ago was 3A and A years correspondingly
Then, (3A + 10) + 10 = 2 [(A + 10) + 10]
3A + 20 = 2A + 40
X = 20
Needed Ratio = (3A + 10) : (A + 10)
= 70 : 30
= 7 : 3
Answer: (A) 7:3
Question: can you find the missing number in the sequence below
11 15 19 12 16 ? 13 17 21 14 18 22
(A) 14
(B) 23
(C) 25
(D) 20
(E) None
Rationale: Correct Answer : D
break the given series
11 15 19
12 16 ?
13 17 21
14 18 22
now read the number from top to bottom
Answer: (D) 20
Question: The speed at which a woman can row a boat in still water is 300 kmph. If he rows downstream, where the speed of current is 42 kmph, what time will he take to cover 190 metres?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Speed of the boat downstream = 300 + 42 = 342 kmph
= 342 * 5/18 = 95 m/s
Hence time taken to cover 190 m = 190/95 = 2 seconds. Answer: B
Answer: (B) 2
Question: A prize of $600 is to be distributed among 15 winners, each of whom must be awarded at least $15. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
(A) $200
(B) $220
(C) $285
(D) $300
(E) $360
Rationale: Total value of the prize =$600
Number of people = 15
2/5 of 600 (=$240) should be distributed among 3/5 of 15 (=9 people ) with each getting $15 each. Remaining money = 600-240 = $360. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $15. Thus, minimising the remaining 5 people (=15-9-1. '-1' to exclude 1 that needs to be maximised) = 5*15=75.
Thus the maximum award can be = 360-75 = $285, hence C is the correct answer.
Answer: (C) $285
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
(A) Rs. 920
(B) Rs. 960
(C) Rs. 1060
(D) Rs. 1200
(E) Rs. 1300
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
ANSWER:B
Answer: (B) Rs. 960
Question: what is rate of interest if principal.amount be 400,simple interest 160 and time 2year.
(A) 10
(B) 12.5
(C) 20
(D) 12
(E) 14.5
Rationale: s.i=(p*r*t)/100
160=800r/100
r=160/8=20%
answer C
Answer: (C) 20
Question: A trade analyst announced 20% reduction in the unit price of car. As a result, the sales volume went up by 5%. What was the net effect on the sales revenue?
(A) no change
(B) decreases by 19.2%
(C) increases by 19%
(D) increases by 19.0%
(E) None of these
Rationale: Explanation :
Reduction of price = (100 -20)% = 80% = 0.8
Increase of sale = (100+5)% = 105% = 1.05
Total effect = 0.8 X 1.01 = 80.8%, Decreases by 19.2%
Answer : B
Answer: (B) decreases by 19.2%
Question: What is the sum of the different positive prime factors of 250?
(A) 10
(B) 11
(C) 15
(D) 7
(E) 18
Rationale: 250
25*10 --> 5*5*2*5 --> 5+2=7. Remember its asking for the DIFFERENT positive prime factors of 250.
D
Answer: (D) 7
Question: If a*b=2a-3b+ab,then3*5+5*3 is equal to
(A) 22
(B) 25
(C) 26
(D) 28
(E) 23
Rationale: 3*5+5*3= (2x3-3x5+3x5)+(2x5-3x3+5x3)
=22
ANSWER A 22
Answer: (A) 22
Question: If logx y = 10 and log2 x = 1000, what is the value of y?
(A) 2100
(B) 21000
(C) 210000
(D) 210
(E) 21100
Rationale: log2 x = 1000
=> x = 21000
logx y = 10
=> y = x10
= (21000)10
= 2(1000 × 10)
= 210000
Answer: Option C
Answer: (C) 210000
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 59.
(A) 1000
(B) 800
(C) 900
(D) 700
(E) 1100
Rationale: Number of odd numbers between 1 and 59 is (59+1)/2=30
Therefore Sum of odd numbers 30*30= 900
ANSWER: C
Answer: (C) 900
Question: Mark is playing poker at a casino. Mark starts playing with 160 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark's remaining chips are $20 chips, how much money did Mark bet?
(A) $1,960
(B) $1,740
(C) $1,540
(D) $3,080
(E) $2,240
Rationale: Total chips 160
20% of $100 chips = 32 chips * $100 = $3,200
80% of $20 chips = 128 chips * $20 = $2,560
If x is the number of chips bet and y is the amount of chips remaining:
x + y = 160
y = 160 - x ~ (1)
[First round bet] + [Second round bet] = $3,200 + $2,560
[0.1x * $100 + 0.9x * $20] + [0.3y * $100 + 0.7y * $20] = $5,760
10x + 18x + 30y + 14y = 5760
28x + 44y = 5760 ~ (2)
Substitute (1) into (2) to solve for x:
28x + 44(160 - x) = 5760
28x + 7040 - 44x = 5760
16x = 1280
x = 80
Substituting x:
[First round bet] = [0.1x * $100 + 0.9x * $20] = 0.1(80)($100)+0.9(80)($20) = $800 + $1,440 = $2,240
Answer is E
Answer: (E) $2,240
Question: If a:b = 3:1, then find (a - 3b)/(2a - b)?
(A) 0
(B) 1
(C) 2
(D) 1/7
(E) 2/7
Rationale: a/b = 3/1 => a = 3b
(a - 3b)/(2a - b) = (3b - 3b)/(6b - b)
= 0/7b => 0
ANSWER:A
Answer: (A) 0
Question: How many times will the digit 8 be written when listing the integers from 1 to 1000?
(A) 164
(B) 297
(C) 300
(D) 345
(E) 482
Rationale: Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 8) 3000/10=300 times.
Answer: C.
Answer: (C) 300
Question: My name is AJEET. But my son accidentally types the name by interchanging a pair of letters in my name. What is the probability that despite this interchange, the name remains unchanged?
A.
B.
C.
D.
(A) 5%
(B) 10%
(C) 20%
(D) 25%
(E) 35%
Rationale: This is a very crude method but i guess it's effective for such small problems.
Possible pairs of letters that could be interchanged are:
AJ
AE
AE
AT
JE
JE
JT
EE
ET
ET
Out of the the ten possibilities, only 1 would lead to an unchanged name.
Therefore, the probability is 1/10 = 10 %.
A more general approach goes as follows:
Each letter can be interchanged in the following ways.
'A' can be interchanged with 4 letters,' 'J' with 3, 'E' with 2 and 'E' with 1.
Therefore total possibilities equal 4+3+2+1=10.
Again only 1 would lead to an unchanged name.
Therefore the answer is 1/10 =10% ANS:B
Answer: (B) 10%
Question: Six years ago, the ratio of the ages of Vimal and Saroj was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Saroj's age at present?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 15
Rationale: Given that, six years ago, the ratio of the ages of Vimal and Saroj =6:5
Hence we can assume that
age of Vimal six years ago =6x
age of Saroj six years ago =5x
After 4 years, the ratio of their ages =11:10
⇒(6x+10):(5x+10)=11:10⇒10(6x+10)=11(5x+10)⇒5x=10⇒x=105=2
Saroj's present age
=(5x+6)=5×2+6=16
Answer is C.
Answer: (C) 16
Question: The remainder when positive integer nn (n>1n>1) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1. What is the least value of nn?
(A) 76
(B) 101
(C) 126
(D) 151
(E) 176
Rationale: We're asked to find the LEAST number that gives us a remainder of 1 when divided by 25 and gives us a remainder of 1 when divided by 7. You might notice, rather quickly, that ALL of the answers gives us a remainder when divided by 25...
76 = 75 + 1
101 = 100 + 1
126 = 125 + 1
151 = 150 + 1
176 = 175 + 1
So the REAL question is "which of these 5 is the least number that has a remainder of 1 when divided by 7?" From here, you can just do the "brute force" math:
A: 76/7 = 10r6 NOT a match
B: 101/7 = 14r3 NOT a match
C: 126/7 = 18r0 NOT a match
D: 151/7 = 21r4 NOT a match
NONE of these numbers "fits" the description, so the answer MUST be E.
E: 176/7 = 25r1;
ANSWER:E
Answer: (E) 176
Question: What is the thousandths digit in the decimal equivalent of 62/5000?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 6
Rationale: 62/5000 = 62 /(5*10^3)
= (62/5) *10^-3
=12.4 * 10^-3
=.0124
Thousandths digit = 2
Answer C
Answer: (C) 2
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
(A) 1100
(B) 1349
(C) 1160
(D) 1450
(E) 1500
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
B
Answer: (B) 1349
Question: If f(x) = k(x - k) and k is a constant, what is the value of f(3) - f(2), in terms of k?
(A)  1
(B)  k
(C)  7k - 1
(D)  k^2 + k
(E)  k^2 - k
Rationale: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(3) and f(2):
f(3) = k(3) - k^2 = 3k - k^2
f(2) = 2k - k^2
f(3)-f(2)=k .. Answer B
Answer: (B)  k
Question: A and B can do a piece of work in 10 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in?
(A) 15.5 days
(B) 4.3 days
(C) 17.5 days
(D) 16.5 days
(E) 18.5 days
Rationale: C = 1/3 – 1/10 = 7/30 => 4.3 days
ANSWER:B
Answer: (B) 4.3 days
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the seven socks?
(A) 12
(B) 15
(C) 21
(D) 36
(E) 42
Rationale: Since given condition that if one sock is on left leg (L) and other colour is on right(R)...and we need to find how many such combinations are possible.
If L has one colour sock and R will have any 6C1 colour sock..
for one combination it is 6 and for seven colour combination it 7*6 = 42.
ANS option E is correct..
Answer: (E) 42
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3 . Find his average after 17th inning.
(A) 39
(B) 88
(C) 26
(D) 87
(E) 11
Rationale: Explanation:
Consider the avg for first 16 innings is x.
Then total runs scored till 16 innings is 16x.
Total runs after 17 innings = 16x + 87.
Thus, 16x+8717=x+316x+8717=x+3 ⇒ x = 36
So his average after 17 innings = 39.
Answer: A
Answer: (A) 39
Question: Sripad has scored average of 62 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?
(A) 79
(B) 70
(C) 38
(D) 27
(E) 21
Rationale: Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 62.
i.e (58+58+x)/3 = 62
116 + x = 186
x = 70 marks.
Therefore, the maximum marks he can score in maths is 70.
Answer: B
Answer: (B) 70
Question: If 3 men or 4 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?
(A) 8/3
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: 3 men can finish a work in 16 days, so in 1 day 3 men finish 1/16th of work and in 1 day 1 men can finish, 1/48th of work.
similarly, in 1 day 1 women can finish 1/64th of work.
12 men in 1 day can finish, 12/48 = 1/4,
8 women in 1 day can finish = 8/64 = 1/8
1/4 + 1/8 = 3/8.
hence number of days to complete is 8/3 days.
ANSWER:A
Answer: (A) 8/3
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 31 years, then find the age of the person sitting in the middle of the row?
(A) 9 years
(B) 29 years
(C) 28 years
(D) 19 years
(E) 17 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (31 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 31 * 3 = 196 - 75 - 93 = 28 years.
ANSWER:C
Answer: (C) 28 years
Question: The prices of a scooter and a television set are in the ratio 3 : 2. If a scooter costs Rs. 6000 more than the television set, the price of the television set is ?
(A) Rs. 6000
(B) Rs. 10000
(C) Rs. 12000
(D) Rs 16000
(E) Rs. 18000
Rationale: Let the price of a scooter be Rs. 3x and that of a television set Rs. 2x.
Then, 3x - 2x = 6000
x = 6000
∴ Cost of a television set = 2x
= Rs. 12000
Answer : C
Answer: (C) Rs. 12000
Question: An emergency vehicle travels 10 miles at a speed of 50 miles per hour. How fast must the vehicle travel on return trip if the round trip travel time is to be 20 minutes?
(A) 75
(B) 26
(C) 20
(D) 12
(E) 91
Rationale: Explanation:
Going trip time = t = dsds = 1050×601050×60 = 12 minutes.
Given total time = 20 minutes
Return trip time = Total time – Going trip time = 20 – 12 = 8 minutes = 860860 hours.
As the distance is 10 miles during even return trip,
The return speed = dtdt = 1086010860 = 10×60810×608 = 75 mph
Answer: A
Answer: (A) 75
Question: What is the difference between the place value and face value of 3 in the numeral 1375?
(A) 296
(B) 297
(C) 298
(D) 29
(E) 31
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
B
Answer: (B) 297
Question: P can do a piece of work in 18 days and Q can do in 22 days, with the help of C, they finish the work in 6 days. How long will it take R to finish the work?
(A) 17days
(B) 18days
(C) 16 ½ days
(D) 17 ½ days
(E) 19 days
Rationale: Explanation:
(P+Q) 1 day work = 1/18 + 1/22 = 7/66
(P+Q+R) 1 day work = 1/6
R 1 day work =1/6 – 7/66 = 2/33
R can do piece of work in 16 ½ days
Answer: Option C
Answer: (C) 16 ½ days
Question: A man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 2.67
(C) 1.2
(D) 1.5
(E) 4
Rationale: M = 12
S = x
DS = 12 + x
US = 12 + x
12 + x = (12 - x)2
12 + x = 24 -2x
3x = 12
x = 4
Answer: E
Answer: (E) 4
Question: The negative number c is divisible by 2. What is the remainder when dividing 5(7-c)(9+c) by 2?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: When we multiply any of these options: 5*11*5 (c=-4) or 5*17*-1 (c=-10) we end up with numbers ending in 5; so any number ending in 5 divided by 2 will always leave a remainder of 1. Hence the correct answer is B.
Answer: (B) 1
Question: Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days.
(A) 11
(B) 12
(C) 13
(D) 15
(E) 16
Rationale: Work done by Kamal in 1 day = 1/20
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days
Answer is E.
Answer: (E) 16
Question: In a 1000 m race, A beats B by 70 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
(A) 145 m
(B) 176 m
(C) 168 m
(D) 163 m
(E) 218 m
Rationale: By the time A covers 1000 m, B covers (1000 - 70) = 930 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/930 * 1000/900 = 1000/837 So, by the time A covers 1000 m, C covers 837 m.
So in 1000 m race A beats C by 1000 - 837 = 163 m.
Answer:D
Answer: (D) 163 m
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 27 (1/3)kmph
(B) 21 (1/3)kmph
(C) 21 (1/7)kmph
(D) 26 (1/3)kmph
(E) 31 (1/3)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.
Answer:B
Answer: (B) 21 (1/3)kmph
Question: The average age of a class of 25 students is 19 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
(A) 40 years
(B) 41 years
(C) 47 years
(D) 43 years
(E) 44 years
Rationale: If age of the teacher was 19, average would not have changed.
Since average increased by 2,
Age of the teacher=25+22×1=47
ANSWER:C
Answer: (C) 47 years
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 (/)
396 11,3,4 (/)
462 11,3 (X)
792 11,3,4 (/)
968 11,4 (X)
2178 11,3 (X)
5184 3,4 (X)
6336 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
B)
Answer: (B) 4
Question: A car takes 4 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 92Kmph
(B) 98Kmph
(C) 90Kmph
(D) 80Kmph
(E) 82Kmph
Rationale: Time = 4
Distence = 540
3/2 of 4 hours = 4 * 3/2 = 6 Hours
Required speed = 540/6 = 90 Kmph
C)
Answer: (C) 90Kmph