mathewhe/aqua_rat huggingface dataset:
Question: Which of the following is closest to the difference between sum W of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
(A) 2.82
(B) 2.72
(C) 1.82
(D) 1.72
(E) 0.82
Rationale: Sum W of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Answer: (D) 1.72
Question: Antonio works in a bakery. He made cookies that cost $2 and made $420. How many customer did he have?
(A) 200 customers
(B) 210 customers
(C) 250 customers
(D) 230customers
(E) 170 customers
Rationale: A cookie costs $2 adding another one is $4. 420 divided by 4 is 105 x 2 is 210. He had 210 customers. The correct answer is B.
Answer: (B) 210 customers
Question: Gold is 11 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 8 times as heavy as water?
(A) 3:2
(B) 1:1
(C) 3:1
(D) 5:2
(E) 4:3
Rationale: G = 11W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
11W+5Wx = x+1 * 8W
11+5x = 8(x+1)
x = 1/1
Ratio of gold with copper = 1:1 = 1:1
Answer is B
Answer: (B) 1:1
Question: A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row?
(A) A)63
(B) B)28
(C) C)48
(D) D)32
(E) E)33
Rationale: Required number of trees
= 24/36 * 42 = 28.
ANSWER:B
Answer: (B) B)28
Question: A Orange costs Rs 11 each and a watermelon costs Rs. 7 each. If I spend Rs 40 on total what is the number of orange I purchased?
(A) 7
(B) 8
(C) 9
(D) 3
(E) 10
Rationale: 3*11 + 7 = 40
Answer : 3
Option : D
Answer: (D) 3
Question: Solve the following quadratic equation by factoring.
x2-5x-14=0
(A) -2,7
(B) 2,-7
(C) 1,8
(D) 1,-8
(E) 2,6
Rationale: We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
(x+2)(x-7)=0
x=-2 and x=7
ANSWER A
Answer: (A) -2,7
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed?
(A) 20km/hr
(B) 30km/hr
(C) 40km/hr
(D) 50km/hr
(E) 90km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 450
50x - 45x = 450
x = 90km/hr
Answer is E
Answer: (E) 90km/hr
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
(A) 10 min
(B) 20 min
(C) 30 min
(D) 40 min
(E) 50 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: (D) 40 min
Question: In how many ways can the letters {U, U, R, R} be arranged?
(A) 4
(B) 20
(C) 120
(D) 720
(E) 840
Rationale: My answer : A
There is 4! ways to arrange those letters in total, however letter U repeats 2! times and letter R repeats 2! times
=> the way to arrange without repeating = 4!/ [2!x2!] = 4
Answer: (A) 4
Question: Calculate the average of all the numbers between 7 and 49 which are divisible by 6.
(A) 20
(B) 18
(C) 19
(D) 15
(E) 30
Rationale: Explanation:
numbers divisible by 6 are 12,18,24,30,36,42,48,
Average = (12+18+24+30+36+42+48, ) / 7 = 210/7 = 30
ANSWER: E
Answer: (E) 30
Question: Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
(A) a) 90
(B) b) 100
(C) c) 110
(D) d) 130
(E) e) 140
Rationale: C. 110
sum of all lengths of all 5 pieces of wood = 128 * 5 = 640
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 640 - 420 = 220
each of these 2 will have length 220/2 = 110
Answer C
Answer: (C) c) 110
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 27 2/23 %
(B) 33 1/3 %
(C) 30%
(D) 19%
(E) 21%
Rationale: Explanation:
100
150
------
150-------50
100-------? => 331/3%
ANSWER IS B
Answer: (B) 33 1/3 %
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 18 kilometer long bridge, at the same speed?
(A) 14 min
(B) 20 min
(C) 18 min
(D) 19 min
(E) 13 min
Rationale: S = 600/40 = 15 mps
S = 18000/15 = 1200 sec = 20 min.Answer: B
Answer: (B) 20 min
Question: How many different ways can you select a pilot and a co pilot if you have 95 people to choose from?
(A) 199
(B) 200
(C) 398
(D) 4950
(E) 8930
Rationale: 1) PERMUTATION:-
since it is selection, we have to find permutation..
95P2= 95!/(95-2)!=8930
ANS:E
Answer: (E) 8930
Question: If x and y are integers such that x^2= y and xy = 343, then x – y = ?
(A) -42
(B) -20
(C) -5
(D) 5
(E) 20
Rationale: here x and y are integers .
x^2=y,xy =343.
substitute x^2=y in xy => x^3=343.
here x^3 is positive ,
x is also positive.
x=7 then y=49.
x-y=-42
so option A is correct
Answer: (A) -42
Question: What is the sum of all the composite numbers up to 18?
(A) 228
(B) 112
(C) 80
(D) 96
(E) 100
Rationale: Explanation:
4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 +18 = 112
Answer: B
Answer: (B) 112
Question: The average successfull Search time for sequential search on n items is
(A) n/2
(B) (n-1)/2
(C) (n+1)/2
(D) log(n)+1
(E) (n)+1
Rationale: To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison.
Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons.
Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons.
so we can write total search time will be: (1+2+3+........+n)
average search time will be (1+2+3+........+n)/n
NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2
ANSWER: C
Answer: (C) (n+1)/2
Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
(A) Rs. 1425
(B) Rs. 1500
(C) Rs. 1537.50
(D) Rs. 1576
(E) Rs. 1643
Rationale: Let the total profit be Rs. 100.
After paying to charity, A's share = Rs. (95 x3/5) = Rs. 57.
If A's share is Rs. 57, total profit = Rs. 100.
If A's share Rs. 855, total profit = (100	x 855/57)	= 1500.
THE CORRECT ANSWER IS B
Answer: (B) Rs. 1500
Question: If a survey shows that 30 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
(A) 56%
(B) 64%
(C) 72%
(D) 82%
(E) 85%
Rationale: Those who support = 30.
% of those who don't support it is (200-30)/ 200 = 85%
Answer E
Answer: (E) 85%
Question: In the parking lot there are 50 vehicles, 30 of them are buses, and the rest are cars. The color of 30 vehicles is red, of which 18 are buses. How many cars can be found in the parking lot which are not colored red?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: The number of cars is 50-30 = 20.
The number of red cars is 30-18=12.
The number of cars which are not red is 20-12=8.
The answer is E.
Answer: (E) 8
Question: there are a no. of chocolates in a bag.if they were equally divided among 14 children,there are 10 chocolates left.if they were to be equally divided among 15 children,there are 8 chocolates left.obviously,this can be satisfied if any multiple of 210 chocolates are added to the bag.What is the remainder when the minimum feasible number of chocolates in the bag is divided by 9
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: let x be the total number of chocolates
14*y1+10=x
15*y1+8=x
so the y1 is 2 and x=38
and 210+38=248
248/9=27 and remainder 5
ANSWER:E
Answer: (E) 5
Question: Find the perimeter and area of a square of side 12 cm.
(A) 144
(B) 121
(C) 169
(D) 196
(E) 100
Rationale: We know that the perimeter of square = 4 Ã— side
Side= 12 cm
Therefore, perimeter = 4 Ã— 12 cm = 48 cm
Now, area of the square = (side Ã— side) sq. units
= 12 Ã— 12 cmÂ²
= 144 cmÂ²
ANSWER : A
Answer: (A) 144
Question: Find the simple interest on Rs. 71,200 at 16 2/3% per annum for 9 months.
(A) s.8500
(B) s.8900
(C) s.7500
(D) s.7000
(E) s.6500
Rationale: P = Rs.71200,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(71,200*(50/3)*(3/4)*(1/100))
= Rs.8900
Answer is B.
Answer: (B) s.8900
Question: Find the unit's digit in the product (2467)^153 * (341)^72
(A) 0
(B) 1
(C) 2
(D) 7
(E) 9
Rationale: unit digit of 341^72 will be 1.
unit digit of (2467)^153 will be same as that of 7^1 (153 mod 4 = 1)
answer 7
ANSWER:D
Answer: (D) 7
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
(A) 12
(B) 16
(C) 20
(D) 24
(E) 48
Rationale: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
answer :E
Answer: (E) 48
Question: The average age of 39 students in a group is 10 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
(A) 50
(B) 55
(C) 60
(D) cannot be determined
(E) None of these
Rationale: Age of the teacher = (40 × 11 – 39 × 10) years
= 50 years.
Answer A
Answer: (A) 50
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.135. How much was lent at 5%?
(A) 2333
(B) 2777
(C) 2688
(D) 1500
(E) 2871
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 135
X = 1500
Answer: D
Answer: (D) 1500
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.8 kmph
(B) 12.7 kmph
(C) 12.6 kmph
(D) 12.5 kilometre per hour
(E) 12.3 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Answer: (D) 12.5 kilometre per hour
Question: In a party every person shakes hands with every other person. If there were a total of 136 handshakes in the party then what is the number of persons present in the party ?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Explanation :
Let the number of persons be n
âˆ´ total handshakes = nC2 = 136
n(n-1)/2 = 136 âˆ´ n = 17
Answer : C
Answer: (C) 17
Question: If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
(A) 141
(B) 200
(C) 618
(D) 391
(E) 412
Rationale: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 618
3A = 612
A = 204
This IS an EVEN INTEGER! The numbers would be 204, 206 and 208. This IS the answer
Final Answer:
C
Answer: (C) 618
Question: What is the remainder when you divide 2^200-2 by 7?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: answer is B. this is very similar to the 32^32^32-2 divided by 7 question.
Answer: (B) 2
Question: A certain list consists of 11 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 10 numbers in the list, then n is what fraction of the sum of the 11 numbers in the list?
(A) 1/3
(B) 2/5
(C) 1/4
(D) 3/5
(E) 1/6
Rationale: series : a1, a2....a10,n
sum of a1+a2+...+a10 = 10*x (x = average)
so, n = 5*x
Hence, a1+a2+..+a10+n = 15x
So, the fraction asked = 5x/15x = 1/3
Answer is A
Answer: (A) 1/3
Question: A clock gains 5 minutes. in 24 hours. It was set right at 10 a.m. on Monday. What will be the true time when the clock indicates 10:30 a.m.on the next Sunday ?
(A) 10 a.m
(B) 11 a.m
(C) 25 minutes past 10 a.m.
(D) 5 minutes to 11 a.m.
(E) None of these
Rationale: Time between 10 a.m. on Monday to 10:30 a.m. on Sunday = 144 1⁄2
24 1⁄2 hours of incorrect clock = 24 hours of correct time.
∴ 1441⁄2 hours of incorrect clock = x hours of correct time.
∴ 144 1/2×24 / 24 1/2=144hoursi.e,
The true time is 10 a.m. on Sunday.
Answer A
Answer: (A) 10 a.m
Question: If m is a positive integer and m^2 is divisible by 39, then the largest positive integer that must divide m is?
(A)  3
(B)  6
(C)  8
(D)  12
(E)  13
Rationale: M^2 is divisible by 48 so M^2 must be multiple of 48.
If the value of M is Multiples of 13 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is E but if M = 39 then answer should be 16.
Is the question right? Or am i missing some thing?
E
Answer: (E)  13
Question: If 893 × 78 = p, which of the following is equal to 893 × 79?
(A)  p + 1
(B)  p + 78
(C)  p + 79
(D)  p + 893
(E)  p + 894
Rationale: Since 893 × 78 = p and 79=78+1, we have 893 × 79 = 893 ×(78+1)=893×78 + 893 ×1 = p + 893.
The answer is (D).
Answer: (D)  p + 893
Question: The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
(A) 74
(B) 94
(C) 184
(D) 364
(E) 154
Rationale: L.C.M. of 6, 9, 15 and 18 is 90. Let required number be 90k + 4, which is multiple of 7. Least value of k for which (90k + 4) is divisible by 7 is k = 4. Required number = (90 x 4) + 4 = 364. Answer :D
Answer: (D) 364
Question: Which of the following fractions is greater than 1/3?
(A) 1. 12/50
(B) 2. 3/11
(C) 3. 2/9
(D) 4. 4/17
(E) 5. 6/24
Rationale: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
A
Answer: (A) 1. 12/50
Question: The music class consists of 3 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
(A) 119
(B) 158
(C) 161
(D) 165
(E) 172
Rationale: Reverse combinatorics approach is preferred method on this one
Note that at least 1 boy gives clue to using this method
All combinations - three girls = answer
All combinations is 10C3 = 120
All girls 3C3 = 1
So our answer is 120-1= 119
Hence, answer is (A)
Answer: (A) 119
Question: Running at the same constant rate, 6 identical machines can produce a total of 420 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 648
(B) 1800
(C) 2800
(D) 10800
(E) 10900
Rationale: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines	6	:	10	:: 420 : x
Time (in minutes)	1	:	4
6 x 1 x x = 10 x 4 x 420
x =	(10 x 4 x 420)/(6)
x = 2800.
ANSWER:C
Answer: (C) 2800
Question: 90 is increased by 50%. Find the final number.
(A) 100
(B) 110
(C) 135
(D) 140
(E) 160
Rationale: Final number = Initial number + 50%(original number) = 90 + 50%(90) = 90 + 45 = 135.
Answer C
Answer: (C) 135
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
(A) 130 kmph
(B) 110 kmph
(C) 150 kmph
(D) 120 kmph
(E) 170 kmph
Rationale: D
120 kmph
Let speed of the car be x kmph.
Then, speed of the train=(150/100)*x=(3/2)*x kmph
(75/x)-(75/(3/2x))=125/(10*60)
(75/x)-(50/x)=5/24
x = 25x24/5 = 120kmph.
Answer: (D) 120 kmph
Question: Carolyn and Sandra are partners in a business. Carolyn manages the business and gets 11% of the profit, and the rest is divided in proportion to their capitals. Find the share of Carolyn's in a profit of 11000 if Carolyn invested 20000 while her partner, Sandra invested 38000.
(A) 6585.9
(B) 2585.9
(C) 1585.9
(D) 3585.9
(E) 4585.9
Rationale: The amount Carolyn gets for managing
= 11% of Rs. 11000 = 1210
Remaining profit = 11000 â€“ 1210 = 9790
This is to be divided in the ratio 20000:38000=20: 38=10:19
Share of Carolyn = 10/29 of 9790 = 3375.9
â‡’ Total share of Carolyn = 1210 + 3375.9 = 4585.9.
Answer E
Answer: (E) 4585.9
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 51.84, the number of the member is the group is:
(A) 57
(B) 67
(C) 72
(D) 87
(E) 97
Rationale: Explanation:
Money collected = (51.84 x 100) paise = 5184 paise.
∴ Number of members = √(5184) = 72.
Answer: C
Answer: (C) 72
Question: Tickets numbered from 1 to 26 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?
(A) 1/5
(B) 2/5
(C) 3/10
(D) 4/13
(E) 1/7
Rationale: Here, S = [1, 2, 3, 4, …., 19, 20, 21, 22, 23, 24, 25, 26]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21, 24]
P (E) = n (E) / n (S) = 8 / 26 = 4/13
The answer is D.
Answer: (D) 4/13
Question: What is the measure of the angle E made by the diagonals of the any adjacent sides of a cube.
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
Rationale: C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60..C
Answer: (C) 60
Question: Pens, Pencils and Markers in a Jenna's desk are in the ratio of 2: 2 : 5. If there are 10 Pens, the number of Markers in Jenna's desk is:
(A) 30
(B) 22
(C) 20
(D) 25
(E) 100
Rationale: Explanation :
Let Pens = 2x, Pencils = 2x & Markers = 5x. Now, 2x = 10 hence x = 5.
Number of markers = 5x which is 25.
Answer : D
Answer: (D) 25
Question: Convert the following unit:
5 hectares in mÂ²
(A) 50000 mÂ²
(B) 40000 mÂ²
(C) 60000 mÂ²
(D) 70000 mÂ²
(E) 55000 mÂ²
Rationale: 5 hectares in mÂ²
1 hectare = 10000 mÂ²
Therefore, 5 hectares = 5 Ã— 10000 mÂ²
= 50000 mÂ²
ANSWER : OPTION A
Answer: (A) 50000 mÂ²
Question: How many times are the hands of a clock at right angle in a day?
(A) 22
(B) 24
(C) 44
(D) 32
(E) 48
Rationale: In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer: Option C
Answer: (C) 44
Question: A train of 30 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 4
(B) 3.3
(C) 5
(D) 7
(E) 9
Rationale: D = 30 * 60 + 1500 = 3300 m
T = 3300/60 * 18/5 = 198 sec = 3.3 mins
Answer: B
Answer: (B) 3.3
Question: The population of a bacteria culture doubles every 6 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
(A) 10
(B) 12
(C) 14
(D) 54
(E) 18
Rationale: This one's easy.
1000 * 2^t = 500,000
2^t = 500
Now gauging, since 2^8 = 256, then 2^9 = 512
So t = 9
But be careful, 't' is in time intervals of 6 minutes
So answer is 9* 6 = 54 minutes
Answer (D)
Answer: (D) 54
Question: Working alone, Mary can pave a driveway in 3 hours and Hillary can pave the same driveway in 6 hours. When they work together, Mary thrives on teamwork so her rate increases by 10%, but Hillary becomes distracted and her rate decreases by 20%. If they both work together, how many hours will it take to pave the driveway?
(A) 2 hours
(B) 4 hours
(C) 5 hours
(D) 6 hours
(E) 7 hours
Rationale: Initial working rates:
Mary = 1/3 per hour
Hillary = 1/6 per hour
Rate when working together:
Mary = 1/3 + (1/10*1/3) = 3/8 per hour
Hillary = 1/6 - (1/5*1/6) = 2/15 per hour
Together they work 3/8 + 2/15 = 1/2 per hour
So they will need 2 hours to complete the driveway. The correct answer is A.
Answer: (A) 2 hours
Question: When positive integer N is divided by positive integer J, the remainder is 15. If N/J = 134.08, what is value of J?
(A) 22
(B) 56
(C) 78
(D) 112
(E) 187.5
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 15
So, 134.08 = 134 + 15/J
So, J = 187.5 ANS E
Answer: (E) 187.5
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
(A) 8 1/8
(B) 8 1/9
(C) 8 1/4
(D) 8 1/1
(E) 8 1/5
Rationale: 3/12 + (3 + x)/15 = 1
x = 8 1/4
Answer:C
Answer: (C) 8 1/4
Question: Four horses are tethered at four corners of a square plot of side 63 metres so that they just cannot reach one another. The area left ungrazed is:
(A) 675.5m2
(B) 780.6m2
(C) 785.8m2
(D) 850.5m2
(E) 950.5m2
Rationale: Required area= (63*63 – 4*1/4 *22/7 * 63/2 * 63/2)= 850.5m2 ANSWER:D
Answer: (D) 850.5m2
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 5 inches wide on each side, the total area would have been (M + 180) square inches. What is the perimeter of the photograph, in inches?
(A) 21
(B) 36
(C) 38
(D) 40
(E) 42
Rationale: Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)
According to the question:
(L+2)(B+2) = m ----(2)
and
(L+10)(B+10) = m + 180 ---------> (L+10)(B+10) - 180 = m ------(3)
Equating (2) and (3)
(L+2)(B+2) = (L+10)(B+10) - 180
LB + 2L + 2B + 4 = LB + 10L + 10B + 100 -180
Simplify
8L + 8B = 84 ------> 2(L+B) = 21 (Check eq (1))
Answer is A
Answer: (A) 21
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE.
(A) 110
(B) 114
(C) 115
(D) 119
(E) 120
Rationale: Total no'of arrangements 5P5 = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114.
B
Answer: (B) 114
Question: Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 23,the first number is :
(A) 22
(B) 21
(C) 77
(D) 99
(E) 26
Rationale: Explanation:
Let the numbers be a,b,c,d
Given, a + b + c = 48, b + c + d = 45
Now, d = 23
thus, b + c + 23 = 45 ⇒ b + c = 22
Putting the value of b + c in a + b + c = 48
a + 22 = 48 ⇒ a = 26
Answer: E
Answer: (E) 26
Question: A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is?
(A) 3kmph
(B) 2.5kmph
(C) 3.5kmph
(D) 4.3kmph
(E) 5kmph
Rationale: Speed of stream = 1/2 (13-8) = 2.5kmph
Answer is B
Answer: (B) 2.5kmph