mathewhe/aqua_rat huggingface dataset:
Question: If the number 892,142,24x is divisible by 11, what must be the value of x?
(A) 1
(B) 2
(C) 3
(D) 0
(E) 5
Rationale: Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
Given number: 892,142,24x
Sum of digits at odd places = 8 + 2 + 4 + 2 + x = 16 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 4 = 16 (ii)
(i) - (ii) = 16 + x - 16 = x - 0
Hence x should be = 0 to make this a multiple of 11 (0) Option D
Answer: (D) 0
Question: When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 24 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?
(A) 30
(B) 34
(C) 42
(D) 48
(E) 50
Rationale: Total # of students 24+28+18-(9+7+10)+4=48.
Answer: D.
Answer: (D) 48
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 20%?
(A) 37.5%
(B) 48%
(C) 50.5%
(D) 52%
(E) 25%
Rationale: Explanation:
Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 80
Gain % = 16/64 * 100 =25%.
Answer: Option E
Answer: (E) 25%
Question: Find a a prime number from the options below.
(A) 69
(B) 70
(C) 71
(D) 72
(E) 74
Rationale: Clearly, 71 is a prime number.
C
Answer: (C) 71
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
(A) 76 kmph
(B) 24 kmph
(C) 99 kmph
(D) 55 kmph
(E) 44 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.Answer:B
Answer: (B) 24 kmph
Question: What is the value of 11^x-11^(x+2), where x is the largest integer such that 11^x is a factor of 30,030?
(A) -1331
(B) -1320
(C) -121
(D) -120
(E) -1
Rationale: The given expression is 11x-11(x^+2) =11x(1-x)
1x needs to be factor of 30030 and x needs to be the largest integer possible. This means 11x needs to be the largest factor possible. The largest factor of a number is the number itself.
The largest factor of 30030 is 30030 = (11 * 2730)
x must be 2730
The value of 11x(1-x) = –1320.
ANSWER:B
Answer: (B) -1320
Question: If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 16 players?
(A) 1245
(B) 1256
(C) 1365
(D) 1370
(E) 1390
Rationale: A particular players is never chosen, it means that 11 players are selected out of 15 players.
=> Required number of ways = 15C11 = 1365
C
Answer: (C) 1365
Question: A 6-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?
(A) 2/3
(B) 3/4
(C) 4/5
(D) 5/6
(E) 6/7
Rationale: The longer wire will form a square with an area more than 1 if the wire is cut at a point within two meters of either end. The probability of this is 4/6 = 2/3.
The answer is A.
Answer: (A) 2/3
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years, The age of the 15th student is
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (14 * 7 + 16 * 7)] = 15 years. Answer: E
Answer: (E) 15
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 110 m
(B) 120 m
(C) 160 m
(D) 180 m
(E) 140 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: B
Answer: (B) 120 m
Question: A sells a bicycle to B at a profit of 30% and B sells it to C at a loss of 20%. Find the resultant profit or loss.
(A) 5%
(B) 4%
(C) -4%
(D) -12%
(E) 2%
Rationale: The resultant profit or loss = 30 - 20 - (30*20)/100 = 4%
profit = 4%
Answer is B
Answer: (B) 4%
Question: If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I. x > y
II. x > y > z
III. x = z
(A) I and II
(B) I only
(C) II only
(D) III only
(E) None
Rationale: If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I. x > y
II. x > y > z
III. x = z
a. I and II
b. I only
c. II only
d. III only
e. None
From the question: we infer that x-y = -z
x,yz are negative integers .
ex: x= -4
y= -6
-4 - (-6) = -(-2). this implies x>y
here x is not equql to z (III)
z>y (II)
So (I) will be answer , SO option B)
Answer: (B) I only
Question: What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (22^2 – 1))
(A) a. 9/19
(B) b. 10/19
(C) c. 10/21
(D) d. 11/23
(E) e. 11/19
Rationale: it can be written into
1/3+1/15+ 1/35.....1/483
i.e
1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/23)
all terms from 1/5 .. to second last term get cancelled
left with
1/3+1/6-1/46=1/2-1/46=22/46=11/23 D
Answer: (D) d. 11/23
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 8610, then what will be the share of Sameer in the profit?
(A) s.2323
(B) s.2940
(C) s.2329
(D) s.2329
(E) s.2312
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 8610 * 14/41
= Rs.2940.
Answer: B
Answer: (B) s.2940
Question: An error 38% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?
(A) 6.64%
(B) 16.64%
(C) 15.64%
(D) 26.64%
(E) 90.44%
Rationale: Percentage error in calculated area
=(38+38+(38Ã—38)/100)%=90.44%
ANSWER:E
Answer: (E) 90.44%
Question: In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
(A) A)60
(B) B)70
(C) C)90
(D) D)120
(E) E)30
Rationale: 6p2 = 6 × 5 x 4 = 120
Option 'D'
Answer: (D) D)120
Question: When n is divided by 19 , the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
(A) 3
(B) 7
(C) 10
(D) 13
(E) nineteen
Rationale: N = 19 q + 6
N = 11 z + 6
Equating
19 Q + 6 = 11z+6
11z=19q
11z/19 = q
since q is an integer Z must be divisible by 19.
ANSWER:E
Answer: (E) nineteen
Question: Twenty four men can do a work in 42 days. How many men are required to complete the work in 36 days?
(A) 20
(B) 28
(C) 50
(D) 40
(E) 60
Rationale: B
28
We have M1 D1 = M2 D2
So, 24 * 42 = M2 * 36 => M2 = 28.
Answer is B
Answer: (B) 28
Question: Find the value of x from (10)^2 x 7^3 Ã· 321 = x.
(A) 106.8
(B) 116.8
(C) 103.8
(D) 126.8
(E) 236.8
Rationale: Given Exp. =(10)^2 x 7^3 Ã· 321 = x
= 100 x 343Ã· 321
106.9
A
Answer: (A) 106.8
Question: There are 6 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
(A) 1/9
(B) 2/9
(C) 5/9
(D) 3/4
(E) 2/3
Rationale: total 8 from take one.
8c1=8
red 6 from one
6c1=6
6/8=3/4
ANSWER:D
Answer: (D) 3/4
Question: In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?
(A) 1 kg
(B) 200gms
(C) 1.8kg
(D) 4.5kg
(E) 500gms
Rationale: There are 200 grams of iron in 1 kg (1,000 grams) of the mixture.
If we add x grams of sand, the total amount would be 1,000 + x grams of mixture and we need 200 grams of iron to be 10% of that: 0.1(1,000 + x) = 200 --> x = 1,000.
Answer: A.
Or: for 200 grams of iron to be 10 of the mixture, the mixture must be 2,000 grams, thus 2,000 - 1,000 = 1,000 grams of sand should be added.
Answer: A.
Answer: (A) 1 kg
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 8000, the number of valid votes that the other candidate got, was:
(A) 3500
(B) 3600
(C) 3270
(D) 3700
(E) 4000
Rationale: Number of valid votes = 80% of 8000 = 6400.
Valid votes polled by other candidate = 45% of 8000
=(45/100)X8000 =3600
ANSWER =B
Answer: (B) 3600
Question: A pipe can empty 2/3rd of a cistern in 12mins. In 6 mins, what part of the cistern will be empty?
(A) 2/3
(B) 3/7
(C) 4/9
(D) 3/8
(E) 1/3
Rationale: 2/3 ---- 12
? ----- 6 ==> 1/3
E
Answer: (E) 1/3
Question: By selling 66 metres of cloth a man loses the selling price of 22 metres. Find the loss percent.
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) None of these
Rationale: Loss = C.P. of 66 metres – S.P. of 66 metres
= S.P. of 22 metres
⇒ C.P. of 66 metres = S.P. of 88 metres
% loss = loss/C.P.of 66metres×100
= S.P.of22metres /C.P.of66metres×100
= S.P.of22metres /S.P.of88metres×100
= 22⁄88 × 100 = 25%
Answer B
* Try to solve by shortcut method
Answer: (B) 25%
Question: Find the odd man out. 241, 263, 248, 271, 255, 277, 262
(A) 277
(B) 271
(C) 263
(D) 241
(E) 248
Rationale: Alternatively 22 is added and 15 is subtracted from the terms. Hence, 271 is wrong
241
241 + 22 = 263
263 - 15 = 248
248 + 22 = 270
270 - 15 = 255
255 + 22 = 277
277 - 15 = 262
Answer is B
Answer: (B) 271
Question: The food in a camp lasts for 25 men for 40 days. If ten more men join, how many days will the food last?
(A) 40 days
(B) 29 days
(C) 60 days
(D) 50 days
(E) 45 days
Rationale: one man can consume the same food in 25*40 = 1000 days.
10 more men join, the total number of men = 35
The number of days the food will last = 1000/35 = 29 days.
ANSWER:B
Answer: (B) 29 days
Question: A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 9/16. How many marbles are in the bag?
(A) 48
(B) 24
(C) 60
(D) 72
(E) 84
Rationale: ok let me see if i can explain what went on in the previous post
lets say i have x marbles in the bag in total --> out of them 12 are red
so the probability of pulling a non-red marble is (x -12) / x
now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x
probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n
so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]
this is given as 9/16
-->(x-12)^2= 16/25
x^2
A
square rooting u have x-12/x = 3/4 or 4x-48 =3x or x = 48
Answer: (A) 48
Question: A farmer had d animals, all of which the farmer bought for the same price. The farmer decided to sell the animals. 22 of the animals were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, the farmer made neither a profit nor a loss. Which of the following is equal to d?
(A) 21
(B) 24
(C) 27
(D) 30
(E) 33
Rationale: Let P be the price the farmer paid for each animal.
The total profit on the 22 animals is 22*0.1*P.
The total loss on the other (d-22) animals is (d-22)*0.2*P.
(d-22)*0.2*P = 22*0.1*P
0.2*d = 2.2 + 4.4
d = 33
The answer is E.
Answer: (E) 33
Question: If a number Q between 0 and 1 is selected at random, which of the following will the number most likely be between?
(A) 0 and 3/20
(B) 3/20 and 1/5
(C) 1/5 and 1/4
(D) 1/4 and 3/10
(E) 3/10 and 1/2
Rationale: The number Q will most likely be between the largest range.
A. 0 and 3/20 --> range 3/20;
B. 3/20 and 4/20 --> range 1/20;
C. 4/20 and 5/20 --> range 1/20;
D. 5/20 and 6/20 --> range 1/20;
E. 6/20 and 10/20 --> range 4/20.
Answer: E.
Answer: (E) 3/10 and 1/2
Question: A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 220 customers. How many more new tables than original tables does the restaurant have?
(A) 10
(B) 20
(C) 30
(D) 34
(E) 36
Rationale: X = Number of original tables
Y = Number of new tables
Capacity of original tables = 4
Capacity of new tables = 6
Total number of tables = X + Y = 40.....(1)
Total capacity = 4X + 6Y = 220.......(2)
(2) - 4*(1) --> 2Y = 60 --> Y = 30, X = 10
How many more new tables than original tables does the restaurant have? --> Y - X = 30 - 10 = 20
Answer: B
Answer: (B) 20
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 72
(B) 70
(C) 60
(D) 85
(E) 90
Rationale: Length = speed*time
S=400/20
s=20 m/sec
Speed = 20*18/5
speed = 72 kmph
ANSWER A
Answer: (A) 72
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 57%
(B) 50%
(C) 52%
(D) 60%
(E) None of these
Rationale: Explanation :
Votes received by the winning candidate = 11628
Total votes = 1136 + 7636 + 11628 = 20400
Required percentage = (11628/20400) × 100 = 11628/204 = 2907/51 = 969/17 = 57%
Answer : Option A
Answer: (A) 57%
Question: If a: b = 10: 9, b: c = 17: 12, find a: b: c?
(A) 150: 143: 118
(B) 160: 173: 128
(C) 170: 153: 108
(D) 180: 163: 138
(E) 190: 183: 148
Rationale: a: b = 10: 9
b: c = 17: 12
a: b: c = 170: 153: 108
ANSWER:C
Answer: (C) 170: 153: 108
Question: Two cars start from the opposite places of a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
(A) 65 km
(B) 75 km
(C) 80 km
(D) 85 km
(E) 95 km
Rationale: 150-((25+25)+35)
ANSWER:A
Answer: (A) 65 km
Question: A hiker walked for 3 days. She walked 25 miles on the first day, walking 5 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
(A) 24
(B) 79
(C) 58
(D) 60
(E) 62
Rationale: She walked 25 miles on the first day, walking 5 miles per hour i.e. total time of walk on Day-1 = 25/5 = 5 Hours
Second day time of walk = 5-1 = 4 hours and Speed = 5+1=6 miles per hour i.e. Distance walked on second day = 4*6 = 24 miles
Third day time of walk = 5 hours and Speed = 6 miles per hour i.e. Distance walked on second day = 5*6 = 30 miles
Total Distance travelled on three days = 25+24+30 = 79
Answer: Option B
Answer: (B) 79
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
(A) 225 cm2
(B) 275 cm2
(C) 285 cm2
(D) 315 cm2
(E) None of these
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
ANSWER:C
Answer: (C) 285 cm2
Question: The dimensions of a rectangular solid are 4 inches, 5 inches, and 12 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
(A)  10:17
(B)  2:5
(C)  5:16
(D)  25:7
(E)  10:21
Rationale: Answer: E.
Answer: (E)  10:21
Question: A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train?
(A) 150 meter
(B) 876 meter
(C) 300 meter
(D) 719 meter
(E) 169 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 18
= 300 meter
Answer: C
Answer: (C) 300 meter
Question: What is the units' digit of the following expression (6)^3*(14)^5*(2)^5?
(A) 0
(B) 1
(C) 3
(D) 5
(E) 8
Rationale: We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 6,14,2 - are EVEN and since the PRODUCT contains 8, the units digit of the product will remain 8
E
Answer: (E) 8
Question: 138.009 + 341.981 – 146.305 = 123.6 + ?
(A) 120.085
(B) 120.85
(C) 220.085
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let 138.009 + 341.981 - 146.305 = 123.6 + x.
Then, x = (138.009 + 341.981) - (146.305 + 123.6) = 479.99 - 269.905 = 210.085 . Answer D
Answer: (D) None of these
Question: My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?
(A) 65
(B) 72
(C) 44
(D) 73
(E) 89
Rationale: B
I am 72 years old.
Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,
365g = 52s.
Since my grandson is 12g months old,
12g = m.
Since my grandson, my son and I together are 120 years,
g + s + m = 120.
The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.
m / 12 + 365 m / (52 x 12) + m = 120 or
52 m + 365 m + 624 m = 624 x 120 or
m = 624 x 120 / 1041 = 72.
So, I am 72 years old.
Answer: (B) 72
Question: The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
(A) 40 years
(B) 42 years
(C) 48 years
(D) 50 years
(E) None
Rationale: Sol.
Therefore age of the mother
= ( 12 × 7 – 7 × 6)
= 42 years.
Answer B
Answer: (B) 42 years
Question: When positive integer w is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: the equation that can be formed w is 13x+2=8y+5..
13x-3=8y...
as we can see x can take only odd values as the RHS will always be even..
Also x can take values till 13 as 13*14>180..
now we have to substitue x as 1,3,5,7,9,11,13...
once we find 7 fitting in , any other value need not be checked as every 4th value will give us answer so next value will be 15..
ans 1.. B
Answer: (B)  1
Question: An article is bought for Rs.635 and sold for Rs.900, find the gain percent?
(A) 30 1/3%
(B) 41 93/127%
(C) 23 1/3%
(D) 35 1/3%
(E) 29 1/3%
Rationale: B
41 93/127%
635 ---- 265
100 ---- ? => 41 93/127%
Answer: (B) 41 93/127%
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 840 in 4 years. The sum is?
(A) s. 738
(B) s. 638
(C) s. 777
(D) s. 730
(E) s. 735
Rationale: S.I. for 1 year = (841 - 825) = Rs. 16
S.I. for 3 years = 16 * 3 = Rs. 48
Principal = (825 - 48) = Rs. 777.
ANSWER:C
Answer: (C) s. 777
Question: A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
(A) 1 hour 37 minutes
(B) 1 hour 40 minutes
(C) 1 hour 20 minutes
(D) 1 hour 30 minutes
(E) 1 hour 23 minutes
Rationale: Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3
=> (5d - 4d)/4k = 1/3 => d = 4/3 k
Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes.
Answer: C
Answer: (C) 1 hour 20 minutes
Question: Train speed 36kph. Dist travelled in 3minutes in meters
(A) 1600
(B) 1700
(C) 1800
(D) 1900
(E) 2000
Rationale: 36kmph=10m/sec
d=10*180=1800 meters
ANSWER:C
Answer: (C) 1800
Question: If f(x)=4x−1 and g(x)=2x+2 for all integers, which of the following is a possible value of g(f(x))?
(A) -23
(B) -17
(C) 2
(D) 16
(E) 20
Rationale: g(f(x)) = 2*f(x)+2 = 2*(4x-1)+2 = 8x
Of these five options, only 16 has the form 8x.
The answer is D.
Answer: (D) 16
Question: Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
(A) R=7
(B) R=4
(C) R=3
(D) R=5
(E) R=2
Rationale: Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R=5
Answer:D
Answer: (D) R=5
Question: Line Y has the equation 3x + y = 7. Which of the following lines is perpendicular to Line Y?
(A)  y = 3x + 4
(B)  y = –3x – 6
(C)  y = (1/3)x – 1
(D)  y = (–1/3)x + 2
(E)  y = (–7/3)x – 5
Rationale: I first rewrote the equation in the standard y=mx+b form. Therefore, Line Y as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line Y? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
Answer: (C)  y = (1/3)x – 1
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120
(B) 277
(C) 288
(D) 265
(E) 291
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2.Answer: A
Answer: (A) 120
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.77 less, he could have gained 25%. What is the cost price?
(A) s.370
(B) s.385
(C) s.375
(D) s.350
(E) s.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
77 ----- ? => 385
ANSWER:B
Answer: (B) s.385
Question: Among 600people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
(A) 20
(B) 60
(C) 80
(D) 150
(E) 180
Rationale: 56%+44%-30%=70% who like either Strawberry, Apple, or both.
That means 100%-70% = 30% do not like either Apple of Strawberry jam.
30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)
E
Answer: (E) 180
Question: a,b,c weighted separately 1st like a, b, c , then a & b, then b & c ,then c & a at last a & b & c, the last weight was 167,then what will be the average weight of the 7 reading?
(A) 95
(B) 95.42
(C) 95.45
(D) 94
(E) 93
Rationale: The sum of 7 weights = weights of[a+b+c+(a+b)+(b+c)+(c+a)+(a+b+c)]= weights of[4*(a+b+c)=4*167=668
Therefore The average weight of 7 readings is 668/7=95.428
ANSWER:B
Answer: (B) 95.42
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
(A) 600
(B) 88
(C) 66
(D) 55
(E) 33
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
Answer: (A) 600
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 11 and 17 is?
(A) 48
(B) 52
(C) 54
(D) 56
(E) 46
Rationale: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 17 will be divided into 3 parts= 11, 3 and 3 (Making one square and two right triangles)
For the right triangle, height will be= (5^2-3^2)^1/2= 4
And the area of trapezoid = 1/2 (B1+B2)H= 1/2*28*4= 56
D is the answer
Answer: (D) 56
Question: The number of sequences in which 4 players can throw a ball, so that the youngest player may not be the last is ?
(A) 24
(B) 22
(C) 10
(D) 16
(E) 18
Rationale: x Not younger
The last ball can be thrown by any of the remaining 4 players. The first 6 players can throw the ball in 3P3 ways.
The required number of ways = 3(3!)
= 18
Answer:E
Answer: (E) 18