mathewhe/aqua_rat huggingface dataset:
Question: x =1 2 3
y= 4 5 18 then what is the relation between x and y
(A) 1*X)^1
(B) 1*X)^6
(C) 1*X)^7
(D) 1*X)^4
(E) 1*X)^2
Rationale: Y=(1*X)^2
4=(1*2)^2
4=4
ANSWER:E
Answer: (E) 1*X)^2
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 6
(D) 5
(E) 1
Rationale: 2x * x = 128 => x
= 8
Answer:A
Answer: (A) 8
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 7
(C) 6
(D) 8
(E) 6
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A
Answer: (A) 4
Question: a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers E was deleted?
(A)  a
(B)  b
(C)  c
(D)  d
(E)  e
Rationale: a+b+c+d+e => 1+2+3+4+5=15
20%*15= 3 =>C
Answer: (C)  c
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it ?
(A) 15 1/3 days
(B) 13 1/3 days
(C) 19 1/3 days
(D) 11 1/3 days
(E) 12 1/3 days
Rationale: B
13 1/3 days
5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer: (B) 13 1/3 days
Question: A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream,it takes 4 hours.What is the speed of the boat in still water ?
(A) 4 km/hr
(B) 6 km/hr
(C) 8 km/hr
(D) Data inadequate
(E) None of these
Rationale: Solution
Rate downstream =(16/2) kmph = 8 kmph, Rate upstream =(16/4) = 4 kmph.
∴ Speed in still water =1/2(8+4) kmph = 6 kmph. Answer B
Answer: (B) 6 km/hr
Question: During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
(A) 714,240
(B) 2,261,760
(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 = 24% greater than the number sold during the first quarter = (1 + 24/100)x = 1.24 x
1.24 x = 2,976,000
=> x = 2,400,000
So, answer will be C
Answer: (C) 2,400,000
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 66 Kmph
(B) 68 Kmph
(C) 86 Kmph
(D) 99 Kmph
(E) 55 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph .Answer: B
Answer: (B) 68 Kmph
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 4 seconds. What is the length of the fast train ?
(A) 22 2/9
(B) 28 7/9
(C) 29 7/9
(D) 30 7/9
(E) None of these
Rationale: Explanation:
As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec
Length of Train= Speed * Time
Length=50/9âˆ—4
=200/9
=22 2/9
Option A
Answer: (A) 22 2/9
Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 9:00 pm and not earlier, when was the drain opened?
(A) at 2:00 pm
(B) at 2:30 pm
(C) at 3:00 pm
(D) at 3:30 pm
(E) at 4:00 pm
Rationale: The filling rate is 1/4 and the draining rate is 1/5.
The combined rate of filling and draining is 1/4 - 1/5 = 1/20.
Let x be the number of hours before the drain was opened.
x/4 + (8-x)/20 = 1
5x + 8 - x = 20
4x = 12
x = 3
The answer is 4:00 pm.
The answer is E.
Answer: (E) at 4:00 pm
Question: A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after 1year service. He served onlyfor 9 months and received uniform & Rs.650, find the price of the uniform?
(A) Rs.90
(B) Rs.100
(C) Rs.150
(D) Rs.190
(E) Rs.200
Rationale: 9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
B
Answer: (B) Rs.100
Question: 9 friends bought a franchise for 500,000 dollars. If they all have to pay the same amount and none of them have bills smaller than $1, how much money would they have to pay?
(A) 500,003
(B) 500,001
(C) 500,004
(D) 500,000
(E) 500,005
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 500,000 = 5 and 9 is divisible by 9.
Hence, we need to add 4 to this number for it to be divisible by 9
Correct Option: C
Answer: (C) 500,004
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
(A) 18
(B) 17
(C) 12
(D) 19
(E) 11
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: (C) 12
Question: What number should replace the question mark?
100, 93, 79, 53, ?.
(A) 30
(B) 36
(C) 32
(D) 41
(E) 44
Rationale: A
30
The sequence progresses –7, –14, –21, –28.
Answer: (A) 30
Question: There are 14 balls in a jar: 8 red, 3 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?
(A) 1/12
(B) 11/14
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: Blue + Red =11
Total number of balls is 8+3+3=14
So the answer is 11/14=11/14
Answer B
Answer: (B) 11/14
Question: Jill, who lives in City C, plans to visit 7 different cities, M, L, P, I, Y, B and S. She plans to visit each city exactly once and return to City C after the 7 visits. She can visit the cities in any order. In how many different orders can she visit the 7 cities?
(A)  3000
(B)  5040
(C)  8000
(D)  9000
(E)  12000
Rationale: 7! = 5040 =B
Answer: (B)  5040
Question: 12 : 21 :: 31 :?
(A) 13
(B) 14
(C) 30
(D) 31
(E) 40
Rationale: Ans 13
Reverse of 31
ANSWER:A
Answer: (A) 13
Question: A man divides $8600 Among 5 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
(A) $200
(B) $1000
(C) $800
(D) $1200
(E) $400
Rationale: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+4*4X+2*X=8600
25X+16X+2X=8600
43X=8600, X=200.
Daughter receives four times of nephew so 4 * 200 = 800.
So Each Daughter receives $800. answer is option C) $800.
Answer: (C) $800
Question: There are three boats B1, B2 and B3 working together they carry 60 people in each trip. One day an early morning B1 carried 50 people in few trips alone. When it stopped carrying the passengers B2 and B3 started carrying the people together. It took a total of 10 trips to carry 300 people by B1, B2 and B3. It is known that each day on an average 300 people cross the river using only one of the 3 boats B1, B2 and B3. How many trips it would take to B1, to carry 150 passengers alone?
(A) 15
(B) 30
(C) 25
(D) 10
(E) 15
Rationale: Explanation:
Combined efficiency of all the three boats = 60 passenger/trip
Now, consider option(a)
15 trips and 150 passengers means efficiency of B1 = 10p/t
which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (10-5 = 5) in which B2 and B3 together carried remaining 250 (300 - 50 = 250) Passengers.
Therefore the efficiency of B2 and B3 = 250/5 = 50 p/t
Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct
Answer: A
Answer: (A) 15
Question: If x and y are integers and xy = 660, x or y must be divisible by which of the following numbers?
(A) 4
(B) 5
(C) 6
(D) 20
(E) 30
Rationale: xy = 660 = 2 * 2 * 3 * 5 * 11
One of x or y must be divisible by 5.
The answer is B.
Answer: (B) 5
Question: Lovely shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
(A) 0.8
(B) 0.75
(C) c) 8/9
(D) 5/7
(E) 6/8
Rationale: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?
In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!
Here's the working:Lovely shop runs a sale on goldfish and platys.
13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2
2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3
8x + 12y = 4.6 [Multiply Equation 3 with 4]
5x = 1.0 [Equation 1 - Equation 2]
x = 0.2
3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]
y = 0.25
x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]
The whole thing must have taken me about 45 s :D
Answer: (D) 5/7
Question: How many solutions does the equation
sin(x) sin(2x) sin(3x) · · · sin(11x) sin(12x) = 0
have in the interval (0,π] ?
(A) 11
(B) 12
(C) 24
(D) 46
(E) 68
Rationale: If x is a solution of the equation, then lx = k for some integers k and l with 1 _<l_<12. Thus
x = k
lπ. Since we want x to be in (0;π], the number of solutions equals the number of fractions in
(0,1] with numerator an integer, and denominator a positive integer _<12. Since we want to avoid
counting the same solution twice (for example 2π/=3 = 4π/6), we need to count only fractions in
lowest terms. Let φ(n) be the number of fractions in lowest terms in (0,1] with denominator n.
Then φ(1) = 1, φ(2) = 1,φ(3) = 2, φ(4) = 2,φ(5) = 4, φ(6) = 2,φ(7) = 6, φ(8) = 4,
φ(9) = 6, φ(10) = 4,φ(11) = 10, and φ'(12) = 4. Adding the above values of φ we get that the
number of solutions is 46.
correct answer D
Answer: (D) 46
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
(A) 4
(B) 10
(C) 15
(D) 16
(E) None
Rationale: L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together 30/2 + 1= 16 times
Answer D
Answer: (D) 16
Question: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 12?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: n = 9x + 6
m = 12y + 4
nm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/12 = (108xy + 36x + 72y + 24)/12
Observe that the all four terms are a multiple of 12
Hence mn/12 will have no remainder
Correct Option: E
Answer: (E) 0
Question: The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/2. What is the probability of Michael passing his driving test?
(A) 1/24.
(B) 2.
(C) 1/3.
(D) 2/3.
(E) 2/5
Rationale: 1/4 *1/m= 1/2 , 1/m = 2
Answer B
Answer: (B) 2.
Question: If $0.90 is the commission for sales of $3,000, what percent of the sales amount is the commission?
(A) 3%
(B) 0.3%
(C) 0.03%
(D) 0.003%
(E) 0.0003%
Rationale: % of sales amount of commission
= (Commission/Total Value) *100
= (0.9/3000) * 100
= 0.03%
The answer is C.
Answer: (C) 0.03%
Question: What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?
(A) 325
(B) 234
(C) 998
(D) 277
(E) 991
Rationale: Let each instalment be Rs.x .
1st year = [x + (x * 12 * 2)/100]
2nd year = [ x + (x *12 * 1)/100]
3rd year = x
Then, [x + (x * 12 * 2)/100] + [ x + (x *12 * 1)/100] + x =1092
3x + ( 24x/100 ) + ( 12x/100 ) = 1092
336x =109200
x = 325
Each instalment = Rs. 325
Answer: A) Rs.325
Answer: (A) 325
Question: A company has 15 managers and 75 associates. The 15 managers have an average salary of $210,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?
(A) $35,000
(B) $45,000
(C) $55,000
(D) $60,000
(E) $75,000
Rationale: Another method is to get ratios
Say 30000=a and
We know the # of people are in 1:5 ratio
Average=(7a*1+a*5)/6= 12a/6=2a=60000
Answer is D. $60,000
Answer: (D) $60,000
Question: If 10 gallons of grape juice are added to 40 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice?
(A) 14%
(B) 25%
(C) 28%
(D) 34%
(E) 50%
Rationale: Mixture contains 4 gallons of grape juice out of 40 gallons
After addition: 14 gallons of grape juice out of 50 gallons ==> 28%
Answer C
Answer: (C) 28%
Question: What will be the compound interest on Rs. 45000 after 3 years at the rate of 12 % per annum
(A) Rs 18221.76
(B) Rs 18123.30
(C) Rs 18123.40
(D) Rs 18123.50
(E) None of these
Rationale: Explanation:
(45000×(1+12/100)3)
=>45000×28/25×28/25×28/25
=>63221.76
So Compound interest will be 63221.76 - 45000
= Rs 18221.76
Option A
Answer: (A) Rs 18221.76
Question: A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.6 million vehicles in 2006, how many vehicles, to the nearest 1,000, did the manufacturer sell in 2007?
(A) 63,000
(B) 2,000,000
(C) 2,030,000
(D) 2,040,000
(E) 2,300,000
Rationale: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.
97/100×2100=2037
-->2,037,000 sold in 2007. When rounded to the nearest 10,000 :
63,000
A
Answer: (A) 63,000
Question: If xy = 5 and x^2 + y^2 = 14, then x/y + y/x =
(A) 2 4/5
(B) 3 1/7
(C) 5 1/3
(D) 7
(E) 60
Rationale: x/y+y/x=(x^2+y^2)/xy =substitute given we get 14/5=2 4/5
answer A
Answer: (A) 2 4/5
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
(A) 9
(B) 11
(C) 13
(D) 15
(E) 12
Rationale: Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3 x = 11.
Third integer = x + 4 = 15.
Answer: D
Answer: (D) 15
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
(A) 10
(B) 99
(C) 88
(D) 77
(E) 66
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
Answer: (A) 10
Question: The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field?
(A) 20
(B) 27
(C) 26
(D) 188
(E) 11
Rationale: Explanation:
Let breadth=x meters.
Then,Length = meters
Given that,
=> x = 20
Breadth = 20
Answer: A) 20 m
Answer: (A) 20
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
(A) 10
(B) 20
(C) 50
(D) 30
(E) 40
Rationale: Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr
Answer is A.
Answer: (A) 10
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) 7219
(B) 3000
(C) 2799
(D) 2797
(E) 2788
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410
= 3000
Answer: B
Answer: (B) 3000
Question: S1 = 3 S2 = 6 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?
(A) 13
(B) 16
(C) 12
(D) 9
(E) 8
Rationale: term 16 = 3*16+4 = 52
Answer : B
Answer: (B) 16
Question: The smallest 3 digit prime number is?
(A) 101
(B) 102
(C) 110
(D) 112
(E) 113
Rationale: The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
A)
Answer: (A) 101
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is?
(A) 4/16
(B) 4/10
(C) 4/11
(D) 4/13
(E) 4/12
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer: D
Answer: (D) 4/13
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which part is not equal to the other four? The number of that part is the answer
(A) x(x + y)2 – 2x2y
(B) x(x + y)2 + 2x2y
(C) x(x2 – y2)
(D) x[(x + y)2 – 2xy]
(E) x[(x + y)2 – 2xy2]
Rationale: Others are x3 + xy2
Answer E
Answer: (E) x[(x + y)2 – 2xy2]
Question: The average of 17 numbers is 10.9. If the average of first nine numbers is 10.5 and that of the last nine numbers is 11.4, the middle number is
(A) 11.8
(B) 11.4
(C) 10.9
(D) 11.7
(E) 11.9
Rationale: Sum of first nine numbers (N1 to N9) + Sum of last nine numbers (N9 to N17) = 10.5 x 9 + 11.4 x 9 = 21.9 x 9 = 197.1
Hence, the middle number
= 197.1 - 17 x 10.9
= 197.1 - 185.3 = 11.8
ANSWER:A
Answer: (A) 11.8
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.60?
(A) 426
(B) 430
(C) 443
(D) 470
(E) 486
Rationale: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 7.6$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.6 $ left. so we buy 1 pack of 50 for 1$. We now have 0.6$ left, so we buy 20 individual envelopes. If we add up the numbers, we get 400+50+20=470 envelopes. Answer D
Answer: (D) 470
Question: If 3a + 1 < 2a < 9 - a, which of the following must be true?
I. -1 < a < 3
II. a < -1
III. a < 3
(A)  II only
(B)  III only
(C)  I and II only
(D)  II and III only
(E)  I, II and III
Rationale: Just try plugging a in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.
So you can immediately cross out any answers with I or III, leaving just (A) II only.
Answer: (A)  II only
Question: In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (4,3) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
(A) (-2,6)
(B) (0,4)
(C) (2,-6)
(D) (2,6)
(E) (4,0)
Rationale: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).
(2,-6) and (2,6) are not on that line. If A is at (0,4) or (3,0), then the area is 1/2*4*3=6. Thus A must be at (2,-6).
Answer: C.
Answer: (C) (2,-6)
Question: A firm has 5 senior partners and 4 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
(A) 70
(B) 75
(C) 80
(D) 85
(E) 90
Rationale: The total number of ways to form a group of 3 is 9C3 = 84
The number of groups without a senior partner is 4C3 = 4
The number of groups which include a senior partner is 84-4 = 80
The answer is C.
Answer: (C) 80
Question: A car is running at a speed of 110kmph. What distance will it cover in 9sec?
(A) 100m
(B) 279m
(C) 180m
(D) 200m
(E) 250m
Rationale: Speed = 110kmph = 110*5/18 = 31 m/s
Distance covered in 9sec = 31*9 = 279m
Answer is B
Answer: (B) 279m
Question: If 34 men do a work in 40 days, in how many days will 20 men do it?
(A) 65
(B) 68
(C) 61
(D) 55
(E) 74
Rationale: 34 * 40 = 20 * x
x = 68 days
Answer: B
Answer: (B) 68
Question: A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?
(A) 210
(B) 252
(C) 280
(D) 300
(E) 420
Rationale: Maximum number of soap boxes that can be placed in each carton = Volume of each carton/ volume of each box
= (25*42*60)/(7*6*5)= 300
ANSWER:D
Answer: (D) 300
Question: Vijay went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19.7
(B) 20.1
(C) 21.4
(D) 21.7
(E) 21.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A)
Answer: (A) 19.7
Question: A pharmaceutical company made 3000 strips of tablets at a cost of Rs. 4800. The company gave away 1000 strips of tablets to doctors as free samples. A discount of 25% was allowed on the printed price. Find the ratio profit if the price is raised from Rs. 3.25 to Rs. 4.25 per strip and if at the latter price, samples to doctors were done away with. (New profit / Old profit).
(A) 55.5
(B) 63.5
(C) 75
(D) 99.25
(E) 80
Rationale: Solution: Total sales revenue (Old) = 2000*3.25*0.75 = 4875[0.75 as 25% discount was allowed]
ProfitOld = Total sales revenue - 4800
= 4875-4800 = 75
Total sales revenue (New) = 3000*4.25*0.75 = 9562.5[New price is calculated on doctors samples as well.]
ProfitNew = 9562.5 - 4800 = 4762.5
Ratio,
ProfitNew / ProfitOld = 4762.5/75 = 63.5.
Answer: Option B
Answer: (B) 63.5
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $20. If the shop keeper has a order of 200 articles, how much profit he will get?
(A) A)200
(B) B)4000
(C) C)1500
(D) D)2000
(E) E)600
Rationale: Total money after selling articles = 200*20 = 4000
cost price = 200*10 = 2000
profit = 2000
correct option is D
Answer: (D) D)2000
Question: 7 points are marked on a straight line and another 8 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
(A) 21
(B) 91
(C) 168
(D) 196
(E) 364
Rationale: select 2 points from one line and one from another.
7C2 * 8C1 [ 2 points from the line containing 7 points and 1 from the line containing 8 points]
+
8C2 * 7C1 [ 2 points from the line containing 8 points and 1 from the line containing 7 points]
=364
ANSWER: [E]
Answer: (E) 364
Question: During a sale, the price of a pair of shoes is marked down 13% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
(A) 9%
(B) 10%
(C) 11%
(D) 15%
(E) 90%
Rationale: Assume the price = 100
Price during sale = 87
Price after sale = 100
Percent increase = 13/87*100 = 15% approx.
Correct Option: D
Answer: (D) 15%
Question: Working alone, A can complete a certain kind of job in 3 hours. A and D, working together at their respective rates, can complete one of these jobs in 2 hours. In how many hours can D, working alone, complete one of these jobs?
(A)  2
(B)  4
(C)  6
(D)  8
(E)  10
Rationale: Let total time taken by D to complete the job = D
total time taken by A to complete the job = 3
Work done by A in an hour
1/A = 1/3
Working together A and D can complete the job in 2 hours
1/A + 1/D = 1/2
=>1/D = 1/2 - 1/A
= 1/2- 1/3
= 1/6
=> D = 6 hours
Answer C
Answer: (C)  6