mathewhe/aqua_rat huggingface dataset:
Question: Today Jim is four times as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 9 times as old as Sam. How old is Jim now?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 40
Rationale: We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is 4 times as old as Fred
2) Today, Sam is 2 years younger than Fred
3) Four years ago, Jim was 9 times as old as Sam.
let's TEST Answer E: 40
IF....Jim is currently 40 years old....
Fred is 10 years old
Sam is 8 years old
4 years ago, Jim was 36 and Sam was 4, so Jim WAS 9 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
E
Answer: (E) 40
Question: The positive two-digit integers m and n have the same digits, but in reverse order. Which of the following must be a factor of m + n?
(A) 33
(B) 9
(C) 10
(D) 12
(E) 14
Rationale: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9
and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187
33 is multiple of 11.
Answer : A
Answer: (A) 33
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 281
(B) 125
(C) 288
(D) 266
(E) 121
Rationale: D = 90 * 5/18 * 5
= 125 m
Answer: B
Answer: (B) 125
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. 1,50,000 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. 150000 x 2/6
= Rs. 50000.
Answer : B
Answer: (B) Rs.50000
Question: Find the sum of all odd numbers upto 100.
(A) 200
(B) 1000
(C) 2500
(D) 3140
(E) 3200
Rationale: Sol. The given numbers are 1, 3, 5, 7, ..., 99.
This is an A.P. with a = 1 and d = 2.
Let it contain n terms. Then,
1 + (n - 1) x 2 = 99 or n = 50.
Required sum = (n/2) (first term + last term)
= 50(1 + 99)/2 = 2500.
ANSWER C 2500
Answer: (C) 2500
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
(A) 16.6
(B) 16.0
(C) 16.3
(D) 16.8
(E) 16.1
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
Answer: D
Answer: (D) 16.8
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 40° is?
(A) 53m2
(B) 51m2
(C) 50.2m2
(D) 45m2
(E) 40m2
Rationale: 40/360 * 22/7 * 12 * 12
= 50.2 m2
Answer:C
Answer: (C) 50.2m2
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 4K – 4 and 5K + 1 is 63, what is the value of K?
(A)  11
(B)  15 3/4
(C)  21
(D)  23
(E)  25 3/10
Rationale: K + 2K +3 + 4K - 4 + 5K +1 = 12K
(12K)/4 = 63
12K = 63 * 4 = 252
K = 252 / 12 = 21
Answer C.
Answer: (C)  21
Question: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 75 with him, what was the average amount with the group before his joining the group?
(A) s. 25.6
(B) s. 45/2
(C) s. 16.6
(D) s. 26
(E) s. 25/2
Rationale: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 50. So, the amount with remaining 6 people = 210 - 75 = Rs. 135
The average amount with them = 135/6 = Rs. 45/2
ANSWER:B
Answer: (B) s. 45/2
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 3 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
(A) 360 km
(B) 480 km
(C) 278 km
(D) 297 km
(E) 671 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 3
2x/15 - x/8 = 3 => x = 360 km.
Answer:A
Answer: (A) 360 km
Question: The sum of the first 50 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?
(A) 5,050
(B) 7,500
(C) 10,500
(D) 15,000
(E) 19,600
Rationale: 101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 50 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 50 positive even integers = 2550
sum of 1st 100 odd numbers = 5050 - 2550 = 2500
so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 2500 = 7500
B is the answer.
Answer: (B) 7,500
Question: The measures of angles A, B and C of a triangle are in the ratio 3:4:5. What is the measure, in degrees, of the largest angle?
(A) 35°
(B) 65°
(C) 85°
(D) 75°
(E) 55°
Rationale: Let the sizes of angles A, B and C be written as follows
A = 3 x, B = 4 x and C = 5 x , where x is a common factor.
The sum of all three angles is equal to 180°. hence
3 x + 4 x + 5 x = 180°
Solve the above equation for x
x = 15
The size of the largest angle is equal to
5 x = 5 * 15 = 75°
correct answer D
Answer: (D) 75°
Question: X does a work in 30 days. Y does the same work in 45 days. In how many days they together will do the same work?
(A) 18
(B) 12
(C) 20
(D) 30
(E) 15
Rationale: X's 1day's work= 1/30
Y's 1 day's work=1/45
(X+Y)'s 1day's work= (1/30+1/45)=1/18
both together will finish the work in 18 days.
correct option is A
Answer: (A) 18
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers
(A) 7
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8
Answer: B
Answer: (B) 8
Question: The amount of time that three people worked on a special project was in the ratio of 1 to 2 to 3. If the project took 120 hours, how many more hours did the hardest working person work than the person who worked the least?
(A) 35 hours
(B) 40 hours
(C) 36 hours
(D) 38 hours
(E) 42 hours
Rationale: Let the persons be A, B, C.
Hours worked:
A = 1*120/6 = 20 hours
B = 2*120/6 = 40 hours
C = 3*120/6 = 60 hours
C is the hardest worker and A worked for the least number of hours. So the difference is 60-20 = 40 hours.
Answer : B
Answer: (B) 40 hours
Question: The simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months. How much amount was borrowed?
(A) 15000
(B) 25000
(C) 7500
(D) 14500
(E) None of these
Rationale: Let the amount be x.
From the question, x×14×6/1200−x×8×8/1200=250
∴ x = 15000
Answer A
Answer: (A) 15000
Question: The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area W of that hemisphere?
(A)  6/π
(B)  9/π
(C)  6
(D)  9
(E)  12
Rationale: Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !!
Answer: (D)  9
Question: If P is a prime number greater than 3, find the remainder when P^2 + 12 is divided by 12.
(A) 6
(B) 1
(C) 0
(D) 8
(E) 7
Rationale: Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 13 = 36N^2 + 12N + 1 + 12 = 36N^2 + 12N + 12 + 1
If P = 6N-1, then P^2 + 13 = 36N^2 - 12N + 1 + 12 = 36N^2 - 12N + 12 + 1
When divided by 12, it must leave a remainder of 1.
The answer is B.
Answer: (B) 1
Question: A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed (in km/hr) must be :
(A) 7 km/hr
(B) 8 km/hr
(C) 11 km/hr
(D) 12 km/hr
(E) None of these
Rationale: Sol.
Remaing distance = 3 km and
Remaining time = [1/3 * 45] min = 15 min = 1/4 hour.
∴ Required speed = (3*4) km/hr = 12 km/hr.
Answer D
Answer: (D) 12 km/hr
Question: What is the value of x if (64^2)-(36^2)=20*x?
(A) 120
(B) 100
(C) 140
(D) 130
(E) 115
Rationale: 20*x=(64+36)(64-36)
20*x=100*28
x=(100*28)/20
x=5*28
x=140
Option C
Answer: (C) 140
Question: Two members of a certain club are selected to speak at the next club meeting. If there are 78 different possible selections of the 2 club members, how many members does the club have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 13
Rationale: Method-1
Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]
i.e. If total member = n
then nC2 = n! / [(2!)(n-2)!] = 78
i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 78
i.e. n*(n-1) = 156
(for Positive Values of n)
therefore, n*(n-1) = 156
i.e. n= 13
Answer: Option E
Answer: (E) 13
Question: A present value of a machine is $128000. Its value depletiation rate is 25% per annum then find the machine value after 3 years
(A) A)$48000
(B) B)$54000
(C) C)$36520
(D) D)$32450
(E) E)$42500
Rationale: P= $128000
R = 25%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=128000*3/4 * 3/4 * 3/4
=$54000
Answer is B
Answer: (B) B)$54000
Question: There are 18 balls in a box: 10 balls are green, 6 are blue and 2 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?
(A) 5/16
(B) 4/13
(C) 3/13
(D) 5/13
(E) 6/13
Rationale: If 1 green and 1 blue ball are taken from the box, then there are 9 green, 5 blue and 2 white balls, a total of 16 balls. If one ball is selected at random, the probability that it is blue is given by 5 / 16
Answer : A
Answer: (A) 5/16
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
(A) 3:4:8
(B) 3:4:7
(C) 3:4:5
(D) 3:4:1
(E) 3:4:0
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
Answer: B
Answer: (B) 3:4:7
Question: In how many ways can three boys can be seated on five chairs?
(A) 72
(B) 28
(C) 60
(D) 58
(E) 39
Rationale: There are three boys.
The first boy can sit in any of the five chairs (5 ways).
5
Now there are 4 chairs remaining. The second boy can sit in any of the four chairs (4 ways).
5	4
Now there are 3 chairs remaining. The third boy can sit in any of the three chairs (3 ways).
5	4	3
Hence, total number of ways in which 3 boys can be seated on 5 chairs
=5×4×3=60
Ans: C
Answer: (C) 60
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
(A) 99
(B) 88
(C) 77
(D) 665
(E) 41
Rationale: 30 * 33/2 = 5/2 * 2 * x => x = 99
Answer:A
Answer: (A) 99
Question: Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 320x is the cube of a positive integer?
(A) 2
(B) 3
(C) 5
(D) 15
(E) 25
Rationale: We want to know the smallest x that will make 320x a CUBE of some number. Let's call that number y.
Let's first figure out what we're working with. The prime factorization of 320 can be visualized:
...........320
......../.......\
......32.......10
...../..\....../...\
...8.....4...2.....5
.../.\ ../.\
..4..2 2..2
./.\
2..2
So, we have 2 * 2 * 2 * 2 * 2 * 2* 5 that can be multiplied together to get 320. Now we need to figure out what we need to make 320 * x into a cube of y (y^3=320*x).
We have six 2s, and one 5. To arrange these numbers in identical triples (2,2,5), we need at least two more 5s. Each of these triples will give us the value of y (2*2*5=20), which, multiplied by itself three times, gives us 320 * x.
Looking at the factors we need to complete the triples, we get 5 * 5 = 25. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.
Therefore, we can go with answer choice E.
If time permits, we can do a sanity check. We calculated that y should be 2 * 2 * 5, or 20. 20 * 20 * 20 = 8000. Also, 320 * 25 = 8000.
Answer: E
Answer: (E) 25
Question: What is the sum of the integers from -150 to 155, inclusive?
(A) 865
(B) 955
(C) 1050
(D) 765
(E) 750
Rationale: In an arithmetic progression,
the nth term is given by tn=a+(n-1)d
here tn=155, a=-150, d=1
hence, 155=-150+(n-1)
or n=306
Sum of n terms can be calculated by sn=n/2(a+l)
a=first term, l=last term, n=no. of terms
sn=306*(-150+155)/2
sn=306*5/2 = 765
Answer : D
Answer: (D) 765
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
(A) 13518
(B) 13519
(C) 13527
(D) 13500
(E) 13521
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer: D
Answer: (D) 13500
Question: . A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
(A) 338
(B) 2767
(C) 1023
(D) 1877
(E) 1722
Rationale: Explanation:
Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer:C
Answer: (C) 1023
Question: Tough and Tricky questions: Word Problems.
It takes Sarah 44 minutes to do one oil change, and it takes Alice 20 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
(A) 10:00 a.m.
(B) 10:42 a.m.
(C) 12:00 a.m.
(D) 12:40 p.m.
(E) 2:00 p.m.
Rationale: LCM of 2044
20 = 2 * 2 * 5
44 = 2 * 2 * 11
LCM = 2 * 2 * 5 * 11 = 220 = 3 hour 40 minutes
1240PM
D
Answer: (D) 12:40 p.m.
Question: A lady grows Broccoli in her garden that is in the shape of a square. Each Broccoli takes 1 square foot of area in her garden. This year, she has increased her output by 79 Broccoli when compared to last year. The shape of the area used for growing the Broccoli has remained a square in both these years. How many Broccoli did she produce this year?
(A) 1600
(B) 1500
(C) 1650
(D) 1700
(E) Cannot be determined
Rationale: Explanatory Answer
The shape of the area used for growing Broccoli has remained a square in both the years.
Let the side of the square area used for growing Broccoli this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing Broccoli last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of Broccoli grown has increased by 79, the area would have increased by 79 sq ft because each Broccoli takes 1 sq ft space.
Hence, X2 - Y2 = 79
(X + Y)(X - Y) = 79.
79 is a prime number and hence it will have only two factors. i.e., 79 and 1.
Therefore, 79 can be expressed as product of 2 numbers in only way = 79 * 1
i.e., (X + Y)(X - Y) = 79 * 1
So, (X + Y) should be 79 and (X - Y) should be 1.
Solving the two equations we get X = 40 and Y = 39.
Therefore, number of Broccoli produced this year = X2 = 402 = 1600.
Alternative Approach : Use answer choices
The area in both the years are squares of two numbers.
That rules out choice B,C and D. as 1500,1650 and 1700 are not the square of any number.
Check Choice A: If this year's produce is 1600, last year's produce would have been 1600 - 79 = 1521
1521 is the square of 39.
So, 1600 is the answer.
Choice A
Answer: (A) 1600
Question: In the xy-plane, line h passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line h?
(A) 3x+2y-5=0
(B) 3x+2y+5=0
(C) 2x-3y-12=0
(D) 2x+3y=0
(E) 4x+3y-6=0
Rationale: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line h should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.
Answer: (A) 3x+2y-5=0
Question: For which of the following functions does f(−z)=−f(z) for all real number values of x?
(A) z^8−z^4
(B) z^5/(z^2+1)
(C) z^5/z^7
(D) z^9/(z^5+1)
(E) z^8
Rationale: all even root cannot be matched eliminated
put z=2
f(−z)=(−2)^5/(−2^)2+1=−32/5, and
−f(z)=−2^5/2^2+1=−32/5, for a match.
ANSWER: B
Answer: (B) z^5/(z^2+1)
Question: 111 = O,
222 = E,
333 = T,
444 = S,
Reading and analyzing the above, can you find out the following ?
555 = ?
(A) 0
(B) 1
(C) 3
(D) 2
(E) 4
Rationale: Solution:
0
Explanation:
1 * 1 * 1 = One
2 * 2 * 2 = Eight
3 * 3 * 3 = Twenty seven
4 * 4 * 4 = Sixty Four
For all the above, you can see that the first letter of the sum is the code.
Thus 5 * 5 * 5 = One twenty five
Thus 555 = O.
Answer A
Answer: (A) 0
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 8 years more than the present age of Anand. Find the present age of Anand?
(A) 12
(B) 14
(C) 15
(D) 16
(E) 18
Rationale: Explanation:
Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 8
Substituting b = a + 8 in first equation,
a - 10 = 1/3 (a -2) => 3a - 30 = a - 2
=> 2a = 28 => a = 14.
Answer: B
Answer: (B) 14
Question: If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?
(A) 17.2
(B) 18.2
(C) 19.2
(D) 15.2
(E) 16.2
Rationale: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 172 in the place of 2994/14.5 ]
= 172/10
= 17.2
Answer is A.
Answer: (A) 17.2
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 18 hrs and a machine of type S does the same job in 9 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) A)3
(B) B)4
(C) C)6
(D) D)9
(E) E)12
Rationale: Rate of machine R =1/18
Rate of machine S =1/9
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/18 +x/9 =1/2
3x/18=1/2
x=18/6=3
So no of machine R is 3
Answer A
Answer: (A) A)3
Question: A vessel of capacity 2 litre has 30% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 30%.
(B) 71%.
(C) 49%.
(D) 29%.
(E) 51%.
Rationale: 30% of 2 litres = 0.6 litres
40% of 6 litres = 2.4 litres
Therefore, total quantity of alcohol is 3.0 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 30%
ANSWER:A
Answer: (A) 30%.
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?
(A) 3
(B) 1/3
(C) 2
(D) 9
(E) 1/9
Rationale: The sum of the first n terms of a G.P. is given by , where 'a' is the first term of the G.P., 'r' is the common ratio and 'n' is the number of terms in the G.P.
Therefore, the sum of the first 6 terms of the G.P will be equal to
And sum of the first 3 terms of the G.P. will be equal to
Use the ratio between these two sums to find 'r'
The ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1
i.e.
Or r3 + 1 = 9
r3 = 8
r = 2
The answer is C
Answer: (C) 2
Question: A tortoise was walking on a 700-feet circular path in a garden at a rate of 100 feet per hour. One hour after the tortoise started, a hare started running from the same starting point on the path at 200 feet per hour. What is the shortest time that the hare could need in order to catch up with the tortoise?
(A) 1 hour
(B) 2 hours
(C) 2.5 hours
(D) 3 hours
(E) 4 hours
Rationale: we don't need to assume here the direction.we need to find which will take less time
so there are 2 cases
1)both moving in same direction...then time would be 1 hour
2)both moving in opposite direction then time would be 2 hours
as we need the shortest time it would be the first case.
Correct answer is A
Answer: (A) 1 hour
Question: A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are fused and he is completely in the dark. How many socks must he take out to make 100 per cent certain he has a pair of black socks?
(A) 10 socks
(B) 20 socks
(C) 30 socks
(D) 40 socks
(E) 50 socks
Rationale: D
40 socks.
If he takes out 38 socks, although it is very unlikely, it is possible they could all be blue and red. To make 100 percent certain that he also has a pair of black socks he must take out a further two socks.
Answer: (D) 40 socks
Question: A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(A) Rs.35
(B) Rs.245
(C) Rs.350
(D) cannot be determined
(E) None of these
Rationale: Explanation:
We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.
Answer: D
Answer: (D) cannot be determined
Question: In a class there are less than 500 students.When it is divided by 3 it gives a whole number. Similarly when it is divided by 4, 5 or 7 gives a whole number. Find the number of students in the class?
(A) 410
(B) 420
(C) 430
(D) 440
(E) 450
Rationale: L.C.M of 3,4,5,7 = 420
ANSWER:B
Answer: (B) 420
Question: A milk man borrowed 2,500 from two money lenders. For one loan, he paid 5% p.a. and for the other, he paid 7% p.a.The total interest paid for two years was 275. How much did he borrow at 7% rate?
(A) 600
(B) 625
(C) 650
(D) 675
(E) None of these
Rationale: Let he borrowed at 5% = x
∴ he borrowed at 7% = (2500 – x)
Now I1 + I2 = 275
x×5×2/100+(2500−x)×7×2/100=275
⇒ 10x + 14(2500 – x) = 27500
⇒ 4x = 35000 – 27500 = 7500
⇒ x = Rs 1875
∴ Sum borrowed at 7% rate = 2500 – 1875 = 625
Answer B
Answer: (B) 625
Question: Sequence G consists of 16 consecutive integers. If -6 is the least integer in sequence G, what is the range of the positive integers in sequence G?
(A)  16
(B)  15
(C)  9
(D)  8
(E)  7
Rationale: Since set G consists of 16 consecutive integers and -6 is the least integer then set G is consecutive integers from -6 to 9, inclusive: 9-(-6)+1=16.
The range of positive integers in sequence G is 9-1=8.
Answer: D.
Answer: (D)  8
Question: Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 49 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
(A) 0.08
(B) 1.0
(C) 1.1
(D) 10.5
(E) 41.8
Rationale: Change in production of motor vehicles = 49 - 3.9 = 45.1 million in 41 years (1987 - 1946)
average increase per year = 45.1/41 = 1.1 million (apporx.)
Answer (C)
Answer: (C) 1.1
Question: When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 86.12, what is the value of y?
(A) 96
(B) 87
(C) 75
(D) 25
(E) 12
Rationale: by the definition of a remainder, the remainder here is equal to 9/y. the remainder in decimal form is given as .12
therefore, 9/y = .12
solve for y and get 75.
C
Answer: (C) 75
Question: During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 30% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
(A) 714,240
(B) 2,289,230
(C) 2,400,000
(D) 3,690,240
(E) 3,915,790
Rationale: Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 30% greater than the number sold during the first quarter = (1 + 30/100)x = 1.3 x
1.3 x = 2,976,000
=> x = 2,289,230
So, answer will be B
Answer: (B) 2,289,230