mathewhe/aqua_rat huggingface dataset:
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270
(B) 288
(C) 266
(D) 299
(E) 126
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer: A
Answer: (A) 270
Question: How many positive integers less than 22 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
(A) 14
(B) 17
(C) 12
(D) 11
(E) 10
Rationale: The number = 2a + 3b < 20
When a = 1, b = 1, 2, 3, 4, 5, 6 -> 2a = 2; 3b = 3, 6, 9, 12, 15, 18 -> the number = 5, 8, 11, 14, 17, 20 --> 6 numbers
when a =2, b = 1,2,3,4,5, 6 -> ....--> 6 numbers
when a =3, b = 1,2,3,4, 5 --> ....--> 5 numbers
Total number is already 17. Look at the answer there is no number greater than 17 --> we dont need to try any more
Answer must be B
Answer: (B) 17
Question: a school has 11 maths 8 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Total subjects = 11+8+5=24
Max subjects by 1 teacher = 3
So, min of teachers required = 24/3 = 8
ANSWER:D
Answer: (D) 8
Question: Find the odd man out. 16, 36, 121, 152, 169, 225, 289, 324
(A) 324
(B) 289
(C) 225
(D) 169
(E) 152
Rationale: Explanation :
Each of the given numbers except 152 is a perfect square
Answer : Option E
Answer: (E) 152
Question: Harish can paint a wall in just 3 hours. However it takes 6 hours for Ganpat to complete the same job of painting the wall.
How long would it take for both of them to paint the wall , if both work together ?
(A) 3 Hours
(B) 1 Hours
(C) 3.20 Hours
(D) 2 Hours
(E) 1.35 Hours
Rationale: D
Two hours.
Harish who could paint the wall in 3 hours could paint 2/3 of the wall in just two hours. Ganpat who paint the wall in 6 hours could paint 1/3 of the wall in two hours.
2/3 + 1/3 = 1.
Answer: (D) 2 Hours
Question: If 2 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
(A)  -7
(B)  -4
(C)  -5
(D)  1
(E)  6
Rationale: The phrase “2 is one solution of the equation” means that one value of x is 2. Thus, we first must plug 2 for x into the given equation to determine the value of k. So we have
2^2 + (3)(2) + k = 10
4 + 6 + k = 10
10 + k = 10
k =0
Next we plug 0 into the given equation for k and then solve for x.
x^2 + 3x = 10
x^2 + 3x – 10 = 0
(x+5)(x-2) = 0
x = -5 or x = 2
Thus, -5 is the other solution. Answer C.
Answer: (C)  -5
Question: Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
(A) $2.50
(B) $5.00
(C) $5.50
(D) $7.50
(E) $15.00
Rationale: Let X be pair of shoes and Y be pair of boots.
22x+16y = 650 ... eq1
8x +32y = 760....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x = 1300
8x = 760.
36x = 540 => x = 15.
Sub x in eq 2.... we get 120 + 32y = 760... then we get 32y = 640 then y = 20
Difference between X and Y is 5.
Answer: option B is correct answer.
Answer: (B) $5.00
Question: A triangle has a perimeter 16. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
(A) 2
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 16
a + 2x = 15.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =6
C
Answer: (C) 6
Question: Larry and Daniel are partners in a business, they invested Rs. 50,000 and Rs. 39,000 respectively.If the business yielded a total profit of Rs. 21,000, what is Daniel's share?
(A) 9402.25
(B) 9272.25
(C) 9982.25
(D) 9211.25
(E) 9202.25
Rationale: Explanation:
Ratio of their shares = 50,000 : 39,000 = 50 : 39.
Daniel's share = Rs. (21000 * 39/89) = Rs. 9202.25.
Answer: E) 9202.25
Answer: (E) 9202.25
Question: If a·b·c·d=360, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?
(A) 9
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: prime factorize : 360 = 2*3*5*12
Hence a = 2 and d = 12 .
Hence answer is 12 - 2 = 10
Answer B
Answer: (B) 10
Question: The maximum number of students among them 1008 pens and 928 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
(A) 16
(B) 18
(C) 36
(D) 19
(E) 32
Rationale: number of pens = 1008
number of pencils = 928
Required number of students = H.C.F. of 1008 and 928 = 16
Answer is A
Answer: (A) 16
Question: Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 1/2 of the juniors is equal to 2/3 of the seniors, what fraction of the students in the room are juniors?
(A) 4/7
(B) 1/3
(C) 5/3
(D) 12/7
(E) 17/20
Rationale: Let total number of juniors= J
total number of seniors =S
(1/2) J = (2/3) S
=> S = 3/4 J
Total number of students = J+S = (7/4) J
Fraction of the students in the room are juniors = J/(J+S) = J/[(7/4) J]
=4/7
Answer A
Answer: (A) 4/7
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-5| + |ab+b| =
(A) ab-4
(B) 2b-ab-4
(C) ab+4
(D) ab-2b+4
(E) 4+2ab
Rationale: Given: |ab| = ab and |a| = -a
Question: |b-5| + |ab+b| = ?
**** Looking at |ab| = ab tells us that a and b are either both positive or negative
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: a and b are both negative values
Let a=-1 and b=-1
|b-5| + |ab+b| = |-1-5| + |1+(-1)| = 6
Test a) ab-4 = (-1)(-1)-4 = -3
Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7
Test c) ab+4 = 1 + 4 = 5
Test d) ab-2b+4 = 1-2(-1)+4=7
test e) 4+2ab= 4+2(-1)(-1)= 6
Answer: E
Answer: (E) 4+2ab
Question: Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage.
(A) 16.8%
(B) 17.4%
(C) 17.9%
(D) 18.5%
(E) 19.1%
Rationale: Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20
Selling price of an orange = 10 --> Cost price = 10/1.25 = 8
A > O
23*(A) + 10*(O) = 653
653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0
Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value
Between 11 and 21, If A = 11, O = 30 --> Not possible
If A = 21, O = 17 --> Possible
Cost price = 20*21 + 8*17 = 420 + 136 = 556
Profit = 653 - 556 = 97
Profit% = (97/556)*100 = 17.4%
Answer: B
Answer: (B) 17.4%
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/7%
(B) 16 6/3%
(C) 16 2/3%
(D) 16 1/3%
(E) 12 2/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: C
Answer: (C) 16 2/3%
Question: Jen has a jar of jam, and she ate 1/3 of the jam for lunch. If Jen ate 1/7 of the remaining jam for dinner, what fraction of the jam was left after dinner?
(A) 2/7
(B) 3/7
(C) 4/7
(D) 9/14
(E) 11/14
Rationale: Let x be the amount of jam at the beginning.
After lunch, the remaining jam was (2/3)x.
After dinner, the remaining jam was (6/7)(2/3)x = (4/7)x.
The answer is C.
Answer: (C) 4/7
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.6
(C) 62.1
(D) 62.7
(E) 62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: (A) 62.5
Question: In a two digit number, the digit in the units place is two times the digit in ten's place and sum of the digits is equal to 12. What is the number?
(A) 25
(B) 28
(C) 32
(D) 36
(E) 48
Rationale: Solution
Let the ten digits be x. Then,units digit=2x
Therefore x + 2x = 12
‹=›3x = 12
‹=›x= 4.
So, ten's digit = 4, unit's digit = 8.
Hence, the required number is 48.
Answer E
Answer: (E) 48
Question: Two whole numbers whose sum is 40 cannot be in the ratio
(A) 4:10
(B) 2:3
(C) 1:3
(D) 2:4
(E) 3:5
Rationale: D) 2:4
Answer: (D) 2:4
Question: The integers from 1 to 1851 are entered sequentially in 12 columns (numbered 1 to 12); i.e. Row 1 contains the numbers 1 to 12, Row 2 contains the next 12 numbers and so on. If the number 1369 occurs in row p and column q, then the value of p + q is
(A) 114
(B) 115
(C) 116
(D) 117
(E) 118
Rationale: 1369=114*12+1
1368=114*12 mean 1368 occurs in 114 row and 12 column.
so 1369 occur in 115 row and 1st column.as elements are entered sequentially.
so p=115 q=1.p+q=116
ANSWER:C
Answer: (C) 116
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *6 + 3 and *6 + 6, inclusive?
(A)  One
(B)  None
(C)  Two
(D)  Three
(E)  Four
Rationale: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *6 would be divisible by all numbers from 1 to 6.
=> *6+3 would give me a number which is a multiple of 3 and therefore divisible (since *6 is divisible by 3)
In fact adding anyprimenumber between 1 to 6 to *6 will definitely be divisible.
So the answer is none (A)!
Supposing if the question had asked for prime numbers between *6 + 3 and *6 + 11 then the answer would be 1. For *6 +3 and *6+ 13, it is 2 and so on...
B
Answer: (B)  None
Question: At 5% per annum simple interest, Rahul borrowed Rs. 500. What amount will he pay to clear the debt after 4 years
(A) 750
(B) 700
(C) 650
(D) 600
(E) None of these
Rationale: Explanation:
We need to calculate the total amount to be paid by him after 4 years, So it will be Principal + simple interest.
So,
=>500+500∗5∗4 /100=>Rs.600
Option D
Answer: (D) 600
Question: A man swims downstream 51 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 2
(B) 8.5
(C) 9.5
(D) 6.5
(E) 11.5
Rationale: 51 --- 3 DS = 17
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (17 + 6)/2 = 11.5
Answer: E
Answer: (E) 11.5
Question: Convert 400 miles into meters?
(A) 784596
(B) 845796
(C) 804670
(D) 784596
(E) 643736
Rationale: 1 mile = 1609.34 meters
400mile = 400*1609.34 = 643736 meters
Answer is E
Answer: (E) 643736
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 3:7
(B) 3:6
(C) 3:1
(D) 3:2
(E) 3:5
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.Answer:C
Answer: (C) 3:1
Question: Rani started a business investing Rs. 10,000. Roja joined him after six months with an amount of Rs. 35,000 and Sachin joined them with Rs. 70,000 after another six months. The amount of profit earned should be distributed in what ratio among Rani, Roja and Sachin respectively, 3 years after started the business ?
(A) 7:6:10
(B) 12:15:16
(C) 42:45:56
(D) None of these
(E) 12 : 35 : 56
Rationale: Explanation :
Akash : Roja : Sachin = (10,000 x 36) : (35,000 x 30) : (70,000 x 24)
= 360 : 1050 : 1680 => 12 : 35 : 56
Answer : E
Answer: (E) 12 : 35 : 56
Question: How many different 6-letter sequences are there that consist of 1A, 20B's and 15C's ?
(A) 6
(B) 60
(C) 120
(D) 360
(E) 720
Rationale: How many different 6-letter sequences are there that consist of 1 A, 20B's, and 15 C's?
(A) 6
(B) 60
(C) 120
(D) 360
(E) 720 (ANS D)
Answer: (D) 360
Question: In an examination 60% failed in Math and 40% failed in French. If 10% failed in both. What % of students passed in both.
(A) 25%
(B) 15%
(C) 20%
(D) 30%
(E) 10%
Rationale: Passed in Math = 100 - 60 = 40%
Passed in French = 100 - 40 = 60%
Students who passed Math or French = 100 -10 = 90%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-90 =10%
ANSWER:E
Answer: (E) 10%
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=ab+ba
II. a@b=(a+b)(a-b-1)
III. a@b=(a/b)+(b/a)
(A) only Ⅰ
(B) only Ⅱ
(C) only Ⅲ
(D) only ⅠⅢ
(E) only ⅡⅢ
Rationale: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b-1)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (X).
Thus, ⅠⅢ are the answers. Therefore, E is the answer.
Answer: (E) only ⅡⅢ
Question: The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.
(A) 3:7
(B) 2:7
(C) 3:5
(D) 5:2
(E) 4:25
Rationale: Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2
= 4x2: 25x2
= 4 : 25.
Ans: E
Answer: (E) 4:25
Question: A volume of 10976 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
(A) 2812
(B) 8231
(C) 2734
(D) 2744
(E) 4254
Rationale: a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 10976l can be kept in (10976/4) hemispheres
ans.2744
ANSWER:D
Answer: (D) 2744
Question: 576, 529, 484, 441, 400, ?
(A) 324
(B) 361
(C) 289
(D) 256
(E) 225
Rationale: Explanation :
The pattern is 24^2, 23^2, 22^2, 21^2, 20^2, ...
So next number is 19^2 = 361
Answer : Option B
Answer: (B) 361
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 9:8
(C) 9:0
(D) 9:5
(E) 9:2
Rationale: Explanation:
Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Answer: Option A
Answer: (A) 9:1
Question: In how many ways can 5 Indians and 5 Englishmen be seated along a circle so that they are alternate?
(A) 6!8!
(B) 4!5!
(C) 3!9!
(D) 8!5!
(E) 7!9!
Rationale: 5 Indians can be seated along a circle in 4! ways
Now there are 5 places for 5 Englishmen
5 Englishmen can be seated in 5! ways
Required number = 4!5!
Answer is B
Answer: (B) 4!5!
Question: The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive?
(A)  5,050
(B)  7,500
(C)  8,050
(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 = 2000
sum of 1st 100 odd numbers = 5050 - 2000 = 3050
so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050
C is the answer.
Answer: (C)  8,050
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
(A) 20%
(B) 18%
(C) 15%
(D) 12%
(E) 10%
Rationale: Answer: Option D
100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
Answer: (D) 12%
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 40% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
(A) 18%
(B) 20%
(C) 21%
(D) 33%
(E) Cannot be determined
Rationale: Answer: D.
Answer: (D) 33%
Question: What is the total number of integers between 100 and 500(exclusive) that are divisible by 5?
(A) 51
(B) 63
(C) 79
(D) 66
(E) 42
Rationale: 105, 110, 115, ..., 490,495
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (495 - 105) / (5) + 1 = 78 + 1 = 79
Answer is C
Answer: (C) 79
Question: Rs.770 were divided among A,B,C in such a way that A had Rs.40 more than B and C had Rs 30 more than A . How much was Bâ€™s share?
(A) Rs.260
(B) Rs.270
(C) Rs.280
(D) Rs.290
(E) Rs.300
Rationale: Let B gets Rs x. Then We can say A gets Rs (x + 40 ) and C gets Rs ( x + 70) .
x + 40 + x + x + 70 = 770
3x = 660
x = 220 .
Bâ€™s share = Rs ( 220 + 70 ) = Rs.290
D
Answer: (D) Rs.290
Question: A student gets 60% in one subject, 70% in the other. To get an overall of 70% how much should get in third subject.
(A) 75%
(B) 80%
(C) 45%
(D) 55%
(E) 65%
Rationale: Let the 3rd subject % = x
60+70+x = 3*70
130+x =210
x = 210-130 = 80
Answer :B
Answer: (B) 80%
Question: In how many ways can the letters L, I, M, I, T, S be arranged so that the two I's are not next to each other?
(A) 36
(B) 48
(C) 240
(D) 296
(E) 428
Rationale: 1 L
2 I
1 M
1 T
1 S
Number of ways these letters can be arranged = 6!/2! (2! to account 2 same Is) = 360
Consider 2 Is as 1 entity and thus the number of arrangements for (II)LMTS = 5! = 120
Total allowed cases = 360-120 =240
C is the correct answer.
Answer: (C) 240
Question: A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
(A) 3.46%
(B) 3.96%
(C) 3.49%
(D) 4.46%
(E) 3.66%
Rationale: Explanation:
Let the original rate be R%. Then, new rate = (2R)%.
Note: Here, original rate is for 1 year(s); the new rate is for only 4 months i.e.1/3 year(s).
(2175 + 725) R = 33.50 x 100 x 3
(2175 + 725) R = 10050
(2900)R = 10050
Original rate = 3.46%
Answer: A) 3.46%
Answer: (A) 3.46%
Question: Solve the given two equations and find the inequality of X and Y. (a) x^2 = 729 and (b) Y= (729)^(1/2)
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=+27, -27 and Y= +27
Comparing we get X<=Y
D
Answer: (D) If x<=y
Question: A light has a rating of 80 watts, it is replaced with a new light that has 25% higher wattage. How many watts does the new light have?
(A) 105
(B) 95
(C) 80
(D) 60
(E) 100
Rationale: Final number = Initial number + 25%(original number) = 80 + 25%(80) = 80 + 20 = 100.
Answer E
Answer: (E) 100
Question: A box contains 25 mangoes out of which 5 are spoilt. If five mangoes are chosen at random, find the probability that A number is selected at random from first fifty natural numbers. What is the chance that it is a multiple of either 7 or 9?
(A) 17/25
(B) 1/25
(C) 6/25
(D) 7/25
(E) 9/25
Rationale: The probability that the number is a multiple of 7 is 7/50. (Since 7*7= 49).
Similarly the probability that the number is a multiple of 9 is 5/50. {Since 9*5 =
45).
Neither 7 nor 9 has common multiple from 1 to 50. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 7 or 9 is (7+5)/50 = 6/25.
ANSWER:C
Answer: (C) 6/25
Question: The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 3.6 miles in the seventh 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?
(A) 33
(B) 36
(C) 39
(D) 42
(E) 45
Rationale: (3.6 miles / 8 minutes)*60 minutes/hour = 27 mph
Let x be the original speed.
x - 6(3) = 27
x = 45 mph
The answer is E.
Answer: (E) 45
Question: 7 members have to be selected from 12 men and 3 women ,Such that no two women can come together .In how many ways we can select them ?
(A) 12c6*3c1 + 12c7
(B) 12c6*3c1 + 2c7
(C) 1c6*3c1 + 12c7
(D) 11c6*3c1 + 12c7
(E) 12c6*3c1 + 11c7
Rationale: since no two women can come together,therfore women can be selected in 3c1 ways ...and men will be chosen in 12c6 so to complete the 7 group members...
=12c6*3c1
and only selection of men also possible = 12c7
so final ans : 12c6*3c1 + 12c7
ANSWER:A
Answer: (A) 12c6*3c1 + 12c7
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
(A) 12 Years
(B) 12.6 Years
(C) 13.6 Years
(D) 14 Years
(E) 14.5 Years
Rationale: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years \
B
Answer: (B) 12.6 Years
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 6 sec
(B) 9 sec
(C) 7 sec
(D) 11 sec
(E) 13 sec
Rationale: Explanation:
T = 60/36 * 18/5 = 6 sec
A)
Answer: (A) 6 sec
Question: Lucy bought a 1-year,10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually. What was the total amount of interest paid on this certificate at maturity ?
.
(A) 10464
(B) 864
(C) 816
(D) 800
(E) 480
Rationale: Solution:
It says, 8 percent per annum per compounded semi annually.
Therefore r = 8/2 = 4% .
So, P = 10000
r = 4
n = 2
Net Amount A = 10816, I = 800.
ANSWER:D
Answer: (D) 800
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 40°, what fraction of the wheel’s area is represented by the smallest sector?
(A) 5/36
(B) 1/36
(C) 1/18
(D) 1/12
(E) 1/9
Rationale: Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 40 --------1
also
a + a+d + a+2d + a+3d +
a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)
which is 8a + 28d = 360 --------2
solving 1 and 2
we get a=50
We are almost done ,
now the question ask what fraction of the wheel’s area is represented by the smallest sector ?
(50/360)( pie r*r)/ (pie r*r) = 50/360= 5/36
A ans ....
Answer: (A) 5/36
Question: In a company of 12 employees, 5 employees earn $36,000, 4 employees earn $45,000, and the 3 highest-paid employees earn the same amount. If the average annual salary for the 12 employees is $47,500, what is the annual salary for each of the highest-paid employees?
(A) $60,000
(B) $65,000
(C) $70,000
(D) $75,000
(E) $80,000
Rationale: 5*36,000+4*45,000+3x=12*47,500
3x=570,000-180,000-180,000
3x=210,000
x=70,000
The answer is C.
Answer: (C) $70,000
Question: If an article is sold at 20% profit instead of 14% profit, then the profit would be Rs. 180 more. What is the cost price?
(A) Rs.1000
(B) Rs. 2000
(C) Rs. 3000
(D) Rs. 4000
(E) Rs.5200
Rationale: Explanation:
Let the cost price of an article be Rs. x.
(20% of x) - (14% of x) = 180
20x/100 - 14x/100 = 105 => 6x = 180 * 100
=> x = 3000
Cost price = Rs. 3000
Answer:C
Answer: (C) Rs. 3000
Question: Pipe P can fill a tank in 16 minutes and pipe Q cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe Q be closed, so that the tank is filled in 30 minutes?
(A) 21
(B) 20
(C) 25
(D) 22
(E) 40
Rationale: 30/16-X/24==>1
X/24=30/16-1==14/16
X=14/16*24 = 21
ANSWER A
Answer: (A) 21
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 10. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 14. How many cooks does the restaurant have?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Originally there were 3k cooks and 10k waiters.
14k = 10k+12
k=3
There are 9 cooks.
The answer is C.
Answer: (C) 9