mathewhe/aqua_rat huggingface dataset:
Question: It's Valentine's day and Alan has promised to cook his girlfriend Alana her favorite meal: fish fingers and custard. Alana will be arriving in one hour exactly. Alan only has a microwave. The fish fingers take 13 minutes to defrost in the microwave and 6 minutes to cook in the microwave. The custard must be prepared after the fish fingers and takes 24 minutes to cook in the microwave and then 6 minutes to cool sufficiently so as not to burn someone's tongue. It will take Alan 1 minute to plate the food. However, Alan is on his Xbox and really wants to play one more game of his football video game before Alana arrives. What is the maximum length of each half of the match that Alan can play to ensure the meal is ready for Alana's arrival?
(A) 5 minutes
(B) 6 minutes
(C) 7 minutes
(D) 8 minutes
(E) 10 minutes
Rationale: Alana will arrive in 60 minutes.
The total meal preparation time is 13 (fish finger defrost) + 6 (fish finger cook) + 24 (custard cook) + 6 (custard cool) + 1 (plate time) = 50 minutes.
Alan therefore has 10 minutes (60-50 = 10) to play his football video game.
As football matches have two halves, Alan have select 5 minute halves (10/2 = 5)
ANSWER: A
Answer: (A) 5 minutes
Question: A contractor is engaged for 30days on the condition that he receives Rs.25 for eachday he works &is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was heabsent?
(A) 5
(B) 10
(C) 17
(D) 25
(E) 30
Rationale: 30 * 25 = 750
425
-----------
325
25 + 7.50 = 32.5
325/32.5 = 10
B
Answer: (B) 10
Question: In the recent, education conference in US, out of 500 men, 800 women, 1000 children present inside the building premises, 30% of the men, 25% of the women and 35% of the children were Russian. Find the percentage of people who were not Russian?
(A) 63.50%
(B) 65.23%
(C) 62.30%
(D) 69.57%
(E) 67.23%
Rationale: Solution: Number of Russian men present there = 500*30/100 = 150
Russian women = 800*25/100 = 200
Russian children = 1000*35/100 = 350.
Total member present in education conference = 500+800+1000 = 2300
Total Russian = 150+200+350 = 700
Hence, % of Russian present there = 700*100/2300 = 30.43%
% of people who were not Russian = 100-30.43 = 69.57%.
Answer D
Answer: (D) 69.57%
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 5 books to the left of the atlas and 4 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
(A) 53
(B) 57
(C) 58
(D) 61
(E) 63
Rationale: 100%. There are total of 30+33-1=62 books and 4+5=9 books are removed, thus 62-9=53 books are left.
Answer: A.
Answer: (A) 53
Question: Suppose that there are n points in the plane and that each of these
points is joined to exactly three of the others by straight line segments.
Then a possible value of n would be
(A) 11
(B) 15
(C) 18
(D) 27
(E) 39
Rationale: Count the number of pairs (p,l) where p is one of the n points and l is a line
segment joining p to one of the other n-1 points. Each point is joined to exactly 3 other
points by line segments so that the total number of pairs is 3n (three line segments for
each of the n points). On the other hand, if there are m total line segments, then each line
segment joins exactly two points so that the total number of pairs (p,l) is 2m (two pointsfor each of the m line segments). Thus, we must have 3n = 2m. But this means that n
must be even. The only even choice given is 18, so this must be the answer.
Is n = 18 really possible or is there some other argument that shows n must be divisible
by 23? One can justify that in fact if n is even, then one can join each of any n points
to 3 of the remaining n - 1 points by line segments. To see this, let n = 2k, and let the
points be p1,..., pn. For each j, join pj by line segments to pj-1, pj+1, and pj+k where
subscripts are to be interpreted modulo n. Thus, for example, if n = 18, then the point
p12 is joined to p11, p13, and p3 (since 12 + 9 + 3 (mod 18)) and the point p1 is joined
to p18 (since 1-1=18 (mod 18)), p2, and p10. You should convince yourself that this
construction for n even joins each point to exactly 3 others.
correct answer C
Answer: (C) 18
Question: A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 40 days, then together ,all will finish the work in :
(A) 13 1/3 days
(B) 12 1/3 days
(C) 15 days
(D) 20 days
(E) 30 days
Rationale: C alone can finish the work in 40 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/40) = 9/120 = 3/40
All the three together will finish it in 40/3 = 13 and 1/3 days.
ANSWER:A
Answer: (A) 13 1/3 days
Question: Tough and Tricky questions: Number Properties.
If (z + 6)/8 is an integer, what is remainder when z is divided by 8?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Assume the answer choices as the value of z
8/8=1
Ans A
Answer: (A) 2
Question: In a group of 58 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
(A) 20
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: Each student is registered forat least one of three classesmeans thatthere are no students who are registered for none of the classes.
Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:
58 = 25 + 25 + 34 - {people in exactly 2 groups} - 2*3 + 0-->{people in exactly 2 groups}=20
Answer: A
Answer: (A) 20
Question: Two cars cover the same distance at the speed of 94 and 90 kmps respectively. Find the distance traveled by them if the slower car takes 2 hour more than the faster car?
(A) 1254
(B) 2827
(C) 2356
(D) 2780
(E) 2614
Rationale: 94(x + 2) = 90x
X = 47
60 * 47 = 2827 km
Answer:B
Answer: (B) 2827
Question: Raju has 6 balls. Out of which 4 green 2 blue. He'll pick 2 balls.. Whats probability dat it contain 1 blue and 1 green..
(A) 7/15
(B) 8/15
(C) 9/15
(D) 11/15
(E) 13/15
Rationale: (2/6*4/5)+ (4/6*2/5)=8/15
ANSWER:B
Answer: (B) 8/15
Question: The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be subtracted. Then,
6 - x
7 - x
<
16
21
21 (6 - x) < 16 (7 - x)
5x > 14
x > 2.8
Least such whole number is 3.
ANSWER:A
Answer: (A) 3
Question: Out of the five integral numbers C is the average of A and D. B is greater than C and less than D.Also B is the average of A and E . The middle most number in the sequence
(A) A
(B) B
(C) J
(D) C
(E) D
Rationale: Explanation:
D _ C _ A --------(1)
D > B > C --------(2)
from (1) and (2)
D > B > C > A ---------(3)
Again E _ B _ A
But B > A, from (3)
So E > D > B > C > A [ Since B is the average of E and A so it is eqidistant from both E and A]
Answer: B
Answer: (B) B
Question: What is the 10 digit to the right of the decimal point, in the decimal expansion of (1/2)^10?
(A)  9
(B)  4
(C)  2
(D)  1
(E)  5
Rationale: Step 1 Convert fraction to decimal with two decimal places 1/2 = 0.50 then convert to scientific number = 5*10^-1
Step 2 Multiply 5^10 by 10^-10
Step 3 5 has the sequence 5, 25, 125
Answer is E
Answer: (E)  5
Question: Two buses of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 10 sec
(B) 30 sec
(C) 40 sec
(D) 20 s
(E) 50 sec
Rationale: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Answer: (D) 20 s
Question: If s is an odd integer, which of the following must also be odd?
(A) 2s + 6
(B) s + s
(C) 3s + 3
(D) 2s + s
(E) s^2 + 1
Rationale: Things to keep in mind:
Odd + odd = even
Odd + even = odd
Odd*odd = odd
Odd*even = even
On checking each option
A. 2s + 6
2s = even, 2s + 6 = even + even = even.
B. s + s
Odd + odd = even. This will be even
C. 3s + 3
3s = odd, 3s + 3 = odd + odd = even
D. 2s + s
2s = even, 2s + s = even + odd = odd
E. s^2 + 1
s^2 = odd, s^2 + 1 = odd + odd = even
Correct option: D
Answer: (D) 2s + s
Question: If the number 481*673 is completely divisible by 9, what is the the smallest whole number in place of *?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let x be the smallest whole number in place of *
481x673 is completely divisible by 9
=> (4+8+1+x+6+7+3) is divisible by 9
=> (29+x) is divisible by 9
x should be the smallest whole number.
Hence, (29+x)=36
=>x=36−29=7
Answer is D.
Answer: (D) 7
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.83200?
(A) 81000
(B) 81028
(C) 105300
(D) 29889
(E) 22312
Rationale: 83200* 9/8 * 9/8 = 105300.Answer:C
Answer: (C) 105300
Question: If two numbers are in the ratio 2:3. If 14 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) A)12
(B) B)18
(C) C)20
(D) D)24
(E) E)28
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 14] = 3[3x + 14]
8x + 56 = 9x + 42
9x - 8x = 56 - 42
x = 14
Then smallest number is = 2
2x = 28
Correct Option E
Answer: (E) E)28
Question: Find the number of divisors of 1080 excluding the divisors which are perfect squares.
(A) 28
(B) 29
(C) 30
(D) 31
(E) 32
Rationale: 1080 = 2^3 *3^3 *5^1
total no. of divisors = (3+1)*(3+1)*(1+1) = 32
only 4 divisors 1, 2^2=4 , 3^2=9 & 2^2*3^2=36 are perfect squares
so,number of divisors excluding perfect squares divisors = 32-4 = 28
ANSWER:A
Answer: (A) 28
Question: In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 65, what is the greatest possible value of B × A?
(A) 0
(B) 5
(C) 10
(D) 15
(E) 25
Rationale: You should notice that 65*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*2=10 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).
Answer: C
!
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C
Answer: (C) 10
Question: Joan and Karl each bought a telescopes and the sum of their purchases was $400. If twice of what Joan paid was $74 more than what Karl paid, what did Joan pay for her telescope?
(A) $150
(B) $152
(C) $154
(D) $156
(E) $158
Rationale: J+K=400 so K=400-J
2J=K+74
2J=(400-J)+74
3J=474
J=158
The answer is E.
Answer: (E) $158
Question: A train 385 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
(A) 5 sec
(B) 21 sec
(C) 7 sec
(D) 10 sec
(E) 52
Rationale: Solution
Speed of train relative to man =(60+6) km/hr= 66km/hr
=(66x5/18) m/sec =(55/3) m/sec
∴ Time taken to pass the man = (385 x 3/55)sec = 21sec
Answer B
Answer: (B) 21 sec
Question: In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 1/2
(E) 2/9
Rationale: P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2
D
Answer: (D) 1/2
Question: Find the fourth proportional to 2.4, 4.6 and 7.6?
(A) 14.56
(B) 15
(C) 15.23
(D) 15.34
(E) 16
Rationale: Formula = Fourth propotional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56
A
Answer: (A) 14.56
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 299
(C) 267
(D) 111
(E) 181
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Answer: (A) 230
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability Y that private Benjamin will be chosen for latrine duty?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: Easier way : Desired probability = 1- 'excluded' probability
In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability Y= 1- 3/5 = 2/5. Thus C is the correct answer.
Answer: (C) 2/5
Question: If 1535/1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?
(A) 165/2
(B) 175/2
(C) 178/3
(D) 187/2
(E) 197/2
Rationale: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Answer: (D) 187/2
Question: A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line.
(A) 10 sec.
(B) 12 sec.
(C) 14 sec.
(D) 16 sec.
(E) None
Rationale: Solution
Speed of the train	= (30 x 5/18)m/sec
= (25 / 3) m/sec.
Distance moved in passing
the standing man	= 100 m.
Required time taken	= 100 /( 25 / 3)
=(100 x 3 / 25) sec
= 12 sec.
Answer B
Answer: (B) 12 sec.
Question: Whats the reminder when 58,458,965,231,457,895,684,525,465,985,445 is divided by 16
(A) 5
(B) 7.
(C) 2.
(D) 3
(E) 9
Rationale: A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16.
Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.
58,458,965,231,457,895,684,525,465,985,445 = 58,458,965,231,457,895,684,525,465,980,000+5,445
The first number is divisible by 16. You just have to find the remainder when you divide 5445 by 16. That will be the remainder when you divide the original number by 16.
5445/16 gives remainder 5.
Answer (A)
Answer: (A) 5
Question: The 3 digits of a number add up to 11. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the 3 digits?
(A) 38
(B) 40
(C) 78
(D) 88
(E) 125
Rationale: xyz is a 3 digit integer divisible by 5. So z can take only 0 or 5. We are also given that x = 2y
This means x+y (2y+y) must be a multiple of 3
xy5 or xy0
CASE 1
x+y+0 = 11
x+y=11
This can't be the case because 11 is not a multiple of 3
CASE 2
x+y+5 = 11
x+y=6
solving we get, x=4y=2
So the 3 digit number is 425
Thus the product of the digits will be = 4 x 2 x 5 = 40
Answer B
Answer: (B) 40
Question: Statement: An earthquake measuring 3.7 hit Delhi and its surrounding areas a little before 3 pm today.
Action:
I. Government should immediately provide financial assistance to the families.
II. People should blame the government for not taking appropriate preventive measures.
(A) Only I follows
(B) Only II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: Explanation:
1st option is not a valid option because financial assistance should be provided by the government but not at this stage. First Priority should be to evacuate people from earthquake hit area.
2nd option is also false because earthquake is a natural disaster. So, blaming government will be of no use.
ANSWER IS D
Answer: (D) Neither I nor II follows
Question: A can finish a piece of work in 4 days. B can do it in 12 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 4 DAYS
(B) 5 DAYS
(C) 6 DAYS
(D) 7 DAYS
(E) 8 DAYS
Rationale: 2/4 + (2 + x)/12 = 1 => x = 4 days
Answer: A
Answer: (A) 4 DAYS
Question: One morning is starts to snow at a constant rate. Later, at 6:00am, a snow plow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time, in other words its speed it inversely proportional to the depth of the snow. If the plow covered twice as much distance in the first hour as the second hour, what time did it start snowing?
(A) 4.15 am
(B) 3.20 am
(C) 5.22 am
(D) 6.10 am
(E) 2.40 am
Rationale: Let the depth of snow at time t to be t units. The speed of the plow at time t will be 1/t. Define t=0 as the time it started snowing and t=x the time the plow started.
The distance covered in the first hour is the integral from x to x+1 of 1/t dt. The antiderivative of 1/t is ln(t) so the total distance covered in the first hour is ln((x+1)/x).
By the same reasoning the distance covered in the second hour in ln((x+2)/(x+1)).
Using the fact that it the plow traveled twice as far in the first hour as the second: ln((x+1)/x) = ln((x+2)/(x+1))2
Exp both sides and you have (x+1)/x = ((x+2)/(x+1))2.
Solving for x you get x=(51/2-1)/2, which is the number of hours that elapsed between the time it started snowing and the snow plow left.It started snowing at (51/2-1)/2 hours before 6:00am, or 5:22:55am.
Answer: (C) 5.22 am
Question: If x+y=17z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
(A)  2z+1
(B)  3z
(C)  6z
(D)  z/3
(E)  3z/2
Rationale: Pick any number like X=12, Y=22 and Z= 2 so that X+Y=17Z, now then the arithmetic mean will be (12+22+2)/3=12. Now, just look at the answers and put the value of Z there.
(A) 2.2+1=5, no
(B) 3.2=6, no
(C) 6.2=12, it can be the answer, lets check us the other options
(D) 2/3, no
(E) (3.2)/2=3, no
so the answer will be C..
Answer: (C)  6z
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 3-letter code words?
(A) 36
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6
# of 3 letter code words:
nPr = 10! / (10 – 3)! = 10*9*8
# of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8) = 42
D
Answer: (D) 42
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?
(A) 7:6
(B) 7:3
(C) 7:4
(D) 7:2
(E) 7:1
Rationale: Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10)
= 70:30
= 7:3
Answer: B
Answer: (B) 7:3
Question: 10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?
(A) 80
(B) 160
(C) 720
(D) 1100
(E) 1260
Rationale: No. of ways of picking 2 biology books(from 10 books) = 10c2 = (10*9)/2 = 45
No. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28
Total ways of picking 2 books of each type = 45*28 =1260
(Option E)
Answer: (E) 1260
Question: A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
(A) Rs. 122
(B) Rs. 121
(C) Rs. 129
(D) Rs. 111
(E) Rs. 191
Rationale: Explanation:
Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]
= [1600 * 41/40(41/40 + 1)
= [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.
C.I. = 3321 - 3200 = Rs. 121.
Answer:B
Answer: (B) Rs. 121
Question: It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?
(A) 15
(B) 19
(C) 12
(D) 17
(E) 10
Rationale: A
Fifteen Minutes.
After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.
Answer: (A) 15
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 13000, then the share of B is?
(A) 6000
(B) 12000
(C) 18000
(D) 24009
(E) 24002
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 13000
Share of B = 6/13 (13000) = Rs. 6000
Answer: A
Answer: (A) 6000
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 9
(B) 8
(C) 5
(D) 2
(E) 1
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Answer: (B) 8
Question: A, E, F, and G ran a race. A said "I did not finish 1st /4th E said "I did not finish 4th" F said "I finished 1st" G said "I finished 4th" If there were no ties and exactly 3 children told the truth, when who finishes 4th?
(A) J
(B) H
(C) K
(D) G
(E) H
Rationale: Answer : D
Answer: (D) G
Question: A batsman makes a score of 95 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
(A) 40
(B) 50
(C) 62
(D) 45
(E) 56
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+95 = 11x
x = 95-50 = 45
Answer is D
Answer: (D) 45
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 25
(B) 35
(C) 75
(D) 80
(E) 90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 3 = 71
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 71 + 4 = 75
C
Answer: (C) 75
Question: A and B start a business jointly. A invests Rs.20000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) A)Rs.12829
(B) B)Rs.16000
(C) C)Rs.12293
(D) D)Rs.12804
(E) E)Rs.12830
Rationale: 20*8: x*4 = 5:2
x = 16 =>
Rs.16000
Answer: B
Answer: (B) B)Rs.16000
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units X digit of (a+2)^2?
(A) 1
(B) 3
(C) 5
(D) 6
(E) C. 14
Rationale: I also got A. By punching in numers:
X...7^2=...9
...8^2=...4
...9^2=...1.A
Answer: (A) 1
Question: Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 1,80,000 earned at the end of 3 years from the start of the business in 2010?
(A) Rs.45000
(B) Rs.50000
(C) Rs.60000
(D) Rs.70000
(E) None of these
Rationale: Explanation :
Aish : Roshan : Atul
= (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1
Roshan's share = Rs. 180000 x 2/6
= Rs. 60000.
Answer : C
Answer: (C) Rs.60000
Question: The average of 5 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 12.5
(B) 26.2
(C) 6.5
(D) 7.5
(E) 12
Rationale: 5 * 15 + 36 – 26
= 75/10
= 7.5
Answer: D
Answer: (D) 7.5