mathewhe/aqua_rat huggingface dataset:
Question: If x/4 years ago Roger was 14 years old and x/4 years from now he will be 4x years old, how old will he be 4x years from now?
(A) 31
(B) 35
(C) 30
(D) 40
(E) 28
Rationale: Assume the current age = a
a - x/4 = 14 (i)
a + x/4 = 4x
Or a = 15x/4 (ii)
Putting the value of a from (ii) in (i)
15x/4 - x/4 = 14
Or 14x/4 = 14 Therefore x = 4 and a = 15
4x years from now, age will be 15 + 4*4 = 31
Option A
Answer: (A) 31
Question: In a forest 110 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
(A) 150
(B) 750
(C) 1,250
(D) 1,500
(E) 2,500
Rationale: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 150 tagged deers comprise 10% of total # of deers --> total # of deers = 110*10 = 1,100.
Answer: D.
Answer: (D) 1,500
Question: Each of the 47 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 14 students sign up for the poetry club, 22 students for the history club, and 20 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The total number in the three clubs is 14+22+20=56.
All 47 students signed up for at least one club.
3 of those students signed up for exactly one more club.
56 - 50 = 6 so 3 students must have signed up for exactly three clubs.
The answer is C.
Answer: (C) 3
Question: The product of x and y is a constant. If the value of x is increased by 30%, by what percentage must the value of y be decreased?
(A) 16%
(B) 23.07%
(C) 25%
(D) 30%
(E) 35%
Rationale: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.3x (130)
i.e. 130*New 'y' = 10000
i.e. New 'y' = 10000/130 = 76.92
i.e. y decreases from 100 to 76.92 i.e. Decrease of 23.07%
B
Answer: (B) 23.07%
Question: Mike's age is 60 years. If he is 3 more than three times the age of his son, find the age of his son.
(A) 25years
(B) 22 years
(C) 20 years
(D) 18 years
(E) 19 years
Rationale: Let Mike's son age be x.
3 + 3x = 60
x = 19
Hence Mike's son age is 19 years
Answer : E
Answer: (E) 19 years
Question: In how many ways can you seat 9 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
(A) 720
(B) 1720
(C) 2880
(D) 5040
(E) 241920
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 6 chairs to sit. The remaining 8 people can sit in 8! ways. Thus the # of arrangements is 6*8! = 241,920.
Answer: E.
Answer: (E) 241920
Question: On multiplying a number by 3, the product is a number each of whose digits is 7. What is the smallest such number?
(A) 259129
(B) 259219
(C) 259279
(D) 259259
(E) None of the above
Rationale: Explanation:
Let's use hit and trial method here.
Smallest number from the given choices = 259129
259129 × 3 = 777387
Next highest number from the given choices = 259219
259219 × 3 = 777657
Next highest number from the given choices = 259259
259259 × 3 = 777777
Hence 259259 is the answer.
Answer: D
Answer: (D) 259259
Question: A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa?
(A) 11/70
(B) 36/91
(C) 21/47
(D) 121/390
(E) 3/71
Rationale: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002
Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792
Hence,Probability=792/2002=36/91
Answer: Option B
Answer: (B) 36/91
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
(A) 12.9
(B) 32.4
(C) 32.1
(D) 32.2
(E) 32.7
Rationale: 36/7 r = 6.3
= 32.4
Answer: B
Answer: (B) 32.4
Question: Find the odd man out
10,20,40,80,90,160
(A) 10
(B) 90
(C) 20
(D) 80
(E) 160
Rationale: 10*2 = 20
20*2 =40
40*2=80
80*2=160
160*2=320
ANSWER:B
Answer: (B) 90
Question: Rs. 6000 is lent out in two parts. One part is lent at 5% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 1:1
(B) 5:6
(C) 5:2
(D) 5:8
(E) 5:2
Rationale: Let the amount lent at 5% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 5/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 3000
Amount lent at 10% = 3000
Required ratio = 1:1
Answer:A
Answer: (A) 1:1
Question: If m and n are positive integers of K such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
(A) 2m/n + 1
(B) 2n/m + 1
(C) 2n/(m+1)
(D) 2m/n
(E) 2n/m
Rationale: Lets say N=10, M=5
2N=20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).
I would choose E.
Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M
Again - Answer is E.
Answer: (E) 2n/m
Question: On the shelf, there are four books of poetry, four novels, and three reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work?
(A) 7/15
(B) 8/25
(C) 9/35
(D) 11/45
(E) 12/55
Rationale: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.
P(one novel and one reference work) = 4/11*3/10 + 3/11*4/10 = 12/55
The answer is E.
Answer: (E) 12/55
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg. What might be the weight of the new person?
(A) 65 kg
(B) 90 kg
(C) 85 kg
(D) Data inadequate
(E) None of these
Rationale: A
65 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (64 + 20) kg = 65 kg.
Answer: (A) 65 kg
Question: Ms. Popez deposits $ 130 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
(A) $118.00
(B) $120.00
(C) $157.30
(D) $122.00
(E) $140.00
Rationale: Using Formula - A = P(1+r/n)^nt
Given
P=130
n=2
t=1
r=0.2
Substituting value in formula
A = 130(1+0.2/2)^2
A= 157.30$=C
Answer: (C) $157.30
Question: Salaries of A, B and C were in the ratio of 3 : 5 : 7 respectively. If their salaries were increased by 50%, 60% and 50% respectively, what will be the new ratio of their respective salaries?
(A) 3 : 6 : 7
(B) 4 : 5 : 7
(C) 4 : 5 : 8
(D) Data inadequate
(E) None of these
Rationale: Suppose the salaries of A, B and C were 300k, 500k and 700k respectively.
After increment salary of
A = 300k + 50% of 300k = 450k
B = 500k + 60% of 500k = 800k
C = 700k + 50% of 700k = 1050k
Hence, new ratio of the respective salaries of A, B and C = 450k : 800k : 1050k = 9 : 16 : 21
Answer E
Answer: (E) None of these
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 192 as interest at the end of the loan period, what was the rate of interest?
(A) 4
(B) 6
(C) 18
(D) Cannot be determined
(E) None of these
Rationale: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 192
=> 12R2= 192
=> R2= 16
=> R= 4
Answer A
Answer: (A) 4
Question: If v=(10^10)-47, what is the sum of all the digit of v?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 80
Rationale: Start small and check for any pattern:
10^2 - 47 = 53 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
10^3 - 47 = 953 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
...extrapolate
10^10 - 47 -> number of digits = 10; number of 9s = 8; 53 will be the last 2 digits
v = 9*8 + 5 + 3 = 80.
Answer (E).
Answer: (E) 80
Question: The difference of the squares of two consecutive even integers is divisible by which of the following numbers?
(A) 4
(B) 3
(C) 7
(D) 6
(E) 9
Rationale: Let the consecutive even integers are n and (n + 2)
difference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1)
which is divisible by 4
Answer is A
Answer: (A) 4
Question: Two trains 170 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9
(B) 10.7
(C) 10.3
(D) 11.88
(E) 12.2
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 170 + 160 = 330 m.
Required time = 330 * 9/250 = 297/25 = 11.88 sec.
'Answer: D
Answer: (D) 11.88
Question: How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?
(A) 24
(B) 30
(C) 56
(D) 120
(E) 216
Rationale: 1) All dice have the same number:
you have 6 possibilities.
2) 2 dice have the same number, but the 3rd is different:
you have 6*5
3) 3 dice are all different:
you have 6*5*4/3! = 20.
Because the question says the order does not matter, u have to divide it by 3!.
so totally you have 56.
ANS:C. 56.
Answer: (C) 56
Question: The sale price sarees listed for Rs.600 after successive discount is 10% and 5% is?
(A) 227
(B) 513
(C) 342
(D) 787
(E) 191
Rationale: 600*(90/100)*(95/100)
= 513
Answer: B
Answer: (B) 513
Question: The cost of 8 sharpeners and 12 pens is Rs.76/-. What is the cost of 20 sharpeners and 30 pens?
(A) Rs.172
(B) Rs.186
(C) Rs.190
(D) Rs.195
(E) Rs.250
Rationale: Explanation:
From the above statement we have,
The cost of 4 sharpeners + 6 pens = Rs.38/-
Multiplying each term by 5, we get
20 sharpeners + 30 pens = Rs.38x5 =Rs.190
Answer: Option C
Answer: (C) Rs.190
Question: By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
(A) Rs. 110
(B) Rs. 120
(C) Rs. 140
(D) Rs. 160
(E) None of these
Rationale: Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
ANSWER:E
Answer: (E) None of these
Question: If r is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
(A) √n + 1
(B) n + 1
(C) n^2 + 1
(D) r + 2√r + 1
(E) n^2 + 2n + 1
Rationale: If r is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
r = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(r) = x
Ans - r + 2 root(r) + 1
This should be D
Answer: (D) r + 2√r + 1
Question: Robert spent $104 in buying raw materials, $175 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
(A) A)$150
(B) B)$210
(C) C)$250
(D) D)$310
(E) E)$200
Rationale: Let the total amount be x
then, (100-10)% of x = 104+175
90% of x = 279
90x/100 = 279
x = $310
Answer is D
Answer: (D) D)$310
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
(A) 40
(B) 42
(C) 43
(D) 45
(E) 50
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
B
Answer: (B) 42
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average
speed for first 320 km of tour.
(A) 70.11 km/hr
(B) 71.11 km/hr
(C) 72.11 km/hr
(D) 73.11 km/hr
(E) None of these
Rationale: Explanation:
We know Time = Distance/speed
So total time taken =
(16064+16080)=92hours Time taken for 320 Km = 320
∗
29=71.11km/hr
Answer: B
Answer: (B) 71.11 km/hr
Question: A no.when divided by 125 gives a remainder 40, what remainder will be obtainedby dividingthe same no.15?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 125 + 40 = 165/15 = 11 (Remainder)
B
Answer: (B) 11
Question: A man bought 10 crates of pine apples for $160 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 30 percent of the total cost?
(A) $36
(B) $46
(C) $26
(D) $16
(E) $6
Rationale: As given, after lost, the remaining 8 crates total cost = $160
So, 1 crate cost = 160/8 =20
To get 30% profit, 1 crate cost should be =20+20*30/100 =$26
Answer : C
Answer: (C) $26
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 14%?
(A) 34.375%
(B) 48%
(C) 50.5%
(D) 52%
(E) 56%
Rationale: Explanation:
Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 86
Gain % = 22/64 * 100 = 34.375%.
Answer: Option A
Answer: (A) 34.375%
Question: How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?
(A) 3587.58
(B) 3587.52
(C) 3587.5
(D) 3587.51
(E) 3587.57
Rationale: I = (8200 * 2.5 * 17.5)/100
= (8200 * 5 * 35)/(100 * 2 * 2)
= Rs. 3587.50
Answer: C
Answer: (C) 3587.5
Question: In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 60%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The tests scores are 4k, 5k, 6k, 7k, and 8k.
The sum of the test scores is 30k.
The average test score is 30k/5 = 60. Then k = 10.
The test scores are 40, 50, 60, 70, and 80.
The student passed 4 subjects.
The answer is D.
Answer: (D) 4
Question: Albert invested Rs. 1000 in a scheme for 3 years at compound interest rate 10% p.a. How much amount will Albert get on maturity of the fixed deposit?
(A) s.1300
(B) s.1005
(C) s.1031
(D) s 1331
(E) s.1120
Rationale: Amount = [1000 * (1 + 10/100)3]
= 1000 * 11/10 * 11/10 * 11/10
= Rs.1331
Answer:D
Answer: (D) s 1331
Question: A club has has $329,864 in its savings account. What is the least amount of money (in whole number of dollars) that must be added to the account the money needs to be spent evenly among nine different scouts for scouting?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount that must be added to the account to split the money evenly among 9 scouts, the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: (D) $4
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 456?
(A) 18%
(B) 26.57%
(C) 20%
(D) 19%
(E) None of these
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 456, Discount = 621 - 456 =165
Discount % = 165/621 * 100 = 26.57%
ANSWER:B
Answer: (B) 26.57%
Question: Find the average of all prime numbers between 30 and 50?
(A) 95.3
(B) 12.8
(C) 75.3
(D) 45.1
(E) 39.8
Rationale: there are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 =199/5 = 39.8.
Ans: E
Answer: (E) 39.8
Question: In how many no. between 100 and 1000 exactly one of the digits is 3?
(A) 648
(B) 512
(C) 252
(D) 225
(E) 26
Rationale: 3 scenarios possible
3XY = 1*9*9 = 81
X3Y (with X ≠≠3 or 0) = 8*1*9 = 72
Y3X (with Y ≠≠3 or 0)= 8*1*9 = 72
Total cases possible = 144+81=225
D is the correct answer
Answer: (D) 225
Question: In a kickball competition of 6 teams, how many possible matches can each team play with each other?
(A)  9
(B)  15
(C)  24
(D)  36
(E)  54
Rationale: 6C2 = 15
Option B
Answer: (B)  15
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6 kmph
(B) 9 kmph
(C) 7 kmph
(D) 5 kmph
(E) 1 kmph
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer:A
Answer: (A) 6 kmph
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6
(B) 6.25
(C) 6.5
(D) 6.75
(E) 7
Rationale: Run rate is calculated by dividing runs scored by the number of overs.
in the first 10 overs there were 32 runs (10*3.2)
282-32=250
250/40=6.25 run rate for the remaining 40 overs
ANSWER : B
Answer: (B) 6.25
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction T of the cookies that were placed in the other tins were placed in the green tin?
(A) 15/2
(B) 9/4
(C) 5/9
(D) 7/5
(E) 9/7
Rationale: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction T= 5N/12 * 12/9N = 5/9 (C)
Answer: (C) 5/9
Question: If 0 < a < b and k = (2a + 5b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k < 9
(D) k > 9
(E) k > 11
Rationale: Here's another approach:
k = (2a + 5b)/b
= 2a/b + 5b/b
= 2(a/b) + 5
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.
So, we get k = (some number less than 2) + 5
From here, we can see that k must be less than 7
Answer: B
Answer: (B) k < 7
Question: what rate percentage is 1 minute 48 seconds to an hour?
(A) 1%
(B) 2%
(C) 3%
(D) 4%
(E) 5%
Rationale: 1m48s =108s
1hr=60m=3600s
% = 108*100/3600 = 3%
ANSWER:C
Answer: (C) 3%
Question: A cube has two of its faces painted half red and half blue. The other faces are completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?
(A) 1:9
(B) 2:3
(C) 2:5
(D) 1:6
(E) 1:4
Rationale: Let x be the area of each face of the cube.
The area painted red is 2(x/2) = x
The area painted white is 4x
The ratio of red to white is x:4x which is 1:4.
The answer is E.
Answer: (E) 1:4
Question: A dealer sold two of his cattle for Rs. 500 each. On one of them he lost 10% on the other, he gained 10%. His gain or loss percent in the entire transaction was:
(A) 10% loss
(B) 1% loss
(C) 1% gain
(D) Neither loss nor profit
(E) 2% gain
Rationale: Explanation:
Loss%= (common gain or loss % / 10)2 = (10/10)² % = 1%. Answer: C
Answer: (C) 1% gain
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 8 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
(A) 0.008
(B) 0.08
(C) 0.064
(D) 0.64
(E) 6.4
Rationale: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*64*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 640/10,000 = 64/1000 = 0.064 ft
The answer is C.
Answer: (C) 0.064
Question: A man with his bike travels to a place 150 km away at an average speed of 50 km per hour and returns at 30 km per hour. His average speed for the whole journey in km per hour is
(A) 35
(B) 37
(C) 37.5
(D) 40
(E) 39
Rationale: Explanation :
Average speed = 2xy/(x + y) km/hr
= 2*50*30/(50 + 30)
= 37.5 km/hr
Answer : C
Answer: (C) 37.5
Question: Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $2 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
(A) $430
(B) $620
(C) $650
(D) $680
(E) $770
Rationale: For 100-40-10=50 pages only cost is 5$ per page for the first time page is typed - 50*5=250$;
For 40 pages the cost is: first time 5$ + 2$ of the first revision - 40*(5+2)=280$;
For 10 pages the cost is: first time 5$ + 2$ of the first revision + 2$ of the second revision - 10(5+2+2)=90$;
Total: 250+280+90=620$.
Answer: B.
Answer: (B) $620
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 20 terms of the arithmetic progression?
(A) 300
(B) 120
(C) 150
(D) 170
(E) 200
Rationale: n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 20 ...we get 20/2[ 2a + 14d] = 20 [a+7d] = 20*10 = 200...
Answer is E...
Answer: (E) 200
Question: The value of x + x(xx) when x = 5 is:
(A) A)36
(B) B)16
(C) C)18
(D) D)130
(E) E)10
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
5 + 5(55)
= 5+ 5(5 × 5)
= 5 + 5(25)
=5 + 125
= 130
D
Answer: (D) D)130
Question: A train 400 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32
(B) 56
(C) 29
(D) 27
(E) 21
Rationale: S = (400 + 300)/45 = 700/45 * 18/5 = 56
Answer: B
Answer: (B) 56
Question: A woman has three blouses of different colors, four skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
(A) 8
(B) 12
(C) 16
(D) 17
(E) 22
Rationale: total ways = 3*4*2=24..
now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..
the ways in which the pink blose and green skirty are together=1*1*2=2..
total ways =24-2=22..
E
Answer: (E) 22
Question: I bought two stocks, for Rs. 500. I sold one at a loss of 20% and other at a gain of 25% and then I found each stick was sold at the same price. Find the cost of the stock sold at a loss?
(A) A)657
(B) B)280
(C) C)438
(D) D)306
(E) E)427
Rationale: x*(80/100)
= (500 - x)125/100
x = 306.4
Answer: D
Answer: (D) D)306
Question: The maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
(A) 91
(B) 40
(C) 80
(D) 90
(E) None of these
Rationale: Solution
Required number of student = H.C.F of 1080 and 920 = 40. Answer B
Answer: (B) 40
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 30,000, B receives:
(A) s. 10,000
(B) s. 10,200
(C) s. 10,400
(D) s. 10,700
(E) s. 10,800
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
B's share = Rs. (30000 x 17/50) = Rs. 10,200.
B
Answer: (B) s. 10,200
Question: A person travels equal distances with speeds of 6km/hr, 12km/hr,18km/hr. and takes a total time of 11minutes. Find the total distance ?
(A) 1km
(B) 1500mts
(C) 1800mts
(D) 2km
(E) 1250mts
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/6)+(x/12)+(x/18) = 11/60
x=0.6
total distance = 3*0.6 = 1.8km = 1800 meters
correct option is C
Answer: (C) 1800mts