mathewhe/aqua_rat huggingface dataset:
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
(A) of these
(B) B)3:5
(C) C)4:3
(D) inadequate
(E) A)3:4
Rationale: Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
ANSWER:A
Answer: (A) of these
Question: 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 20
(B) 10
(C) 30
(D) 40
(E) 50
Rationale: C
30
3W = 2M
15M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
15 * 21 * 8 = 14 * x * 6
x = 30
Answer: (C) 30
Question: If the ratio of the roots of the equation 4x2-px+8=0 is equal to that of the roots 2x2-rx+16=0, then:
(A) 4r=p
(B) r=p
(C) 2r=p
(D) 2p=r
(E) None
Rationale: 4x2-px+8=0 for this eqn... roots are R1=p/4 R2=-2
2x2-rx+16=0 for this eqn... roots are R3=r/2 R4=-8
As per Question, p/-8=r/-16
=> 2p=r
ANSWER:D
Answer: (D) 2p=r
Question: The present worth of $3600 due in 2 years at 20% per annum compound interest is?
(A) $1200
(B) $1850
(C) $2010
(D) $3200
(E) $2500
Rationale: Present worth = 3600/ (1 + 20/100)^2 = 3600 * 5/6 * 5/6 = $2500
Answer is E
Answer: (E) $2500
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 75
(B) 87
(C) 68
(D) 99
(E) 32
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2
= 75.
Answer:A
Answer: (A) 75
Question: During 2003, a company produced an average of 3,000 products per month. How many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 300% over its 2003 average?
(A) 520,000
(B) 540,000
(C) 525,000
(D) 530,000
(E) 550,000
Rationale: Company produced 12*3000 = 36,000 products in 2003. If company produces X products from 2004 to 2007, then total amount of product produced in 4 years (2003 through 2007) is X+36,000. The gives the average of (X+36,000)/4.
This average needs to be 300% higher than that in 2003. In math terms, 36,000+300%(36,000) = 144,000. So:
(X+36,000)/4 = 144,000
X+36,000 = 576,000
X = 540,000
The answer is B.
Answer: (B) 540,000
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
(A) 399
(B) 400
(C) 2887
(D) 277
(E) 1213
Rationale: 441 = P(21/20)2
P = 400.Answer: B
Answer: (B) 400
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 18. The larger of the two numbers is:
(A) 276
(B) 414
(C) 322
(D) 345
(E) 355
Rationale: Clearly, the numbers are (23 x 13) and (23 x 18).
Larger number = (23 x 18) = 414. Answer: Option B
Answer: (B) 414
Question: what is the remainder when 7^700 is divided by 100?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (7^700)mod100= [7^(2*350)]mod100=[49^350]mod100=[(50-1)^350]mod100=[{350C349}*50*(-1)^349 +350C350*(-1)^350]mod100 = [-350*50+1]mod100=1mod100
So, evidently, the remainder will be 1.
ANSWER:A
Answer: (A) 1
Question: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 33rd in an arithmetic progression if the sum of the 15th and 19th terms of the sequence is 108?
(A) 38
(B) 42
(C) 46
(D) 50
(E) 54
Rationale: Let x be the difference between any two consecutive terms.
The mean of a sequence like this is the middle term, thus the 17th term in the sequence.
Then the mean of the 16th and 18th term is also equal to the overall mean, because the 16th term is (17th term - x) and the 18th term is (17th term + x).
Similarly the mean of the 15th and 19th term is also equal to the mean.
etc...
Thus the mean is 108/2 = 54
The answer is E.
Answer: (E) 54
Question: The circumferences of two circles are 528 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 29963 sq m
(B) 28937 sq m
(C) 43162 sq m
(D) 27688 sq m
(E) 17248 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 528 and 2∏l = 704
s = 528/2∏ and l = 704/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{264^2/∏^2 - 352^2/∏^2}
= 264^2/∏ - 352^2/∏
= (264 - 352)(264 + 352)/∏
= (88)(616)/(22/7)
=17248 sq m
Answer:E
Answer: (E) 17248 sq m
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 5 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
(A) 18 : 35 : 50
(B) 3 : 10 : 10
(C) 4 : 8 : 5
(D) 32 : 35 : 25
(E) None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 8x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 5x × 140% :
8x × 125% = 36 : 70 : 100
= 18 : 35 : 50
Answer A
Answer: (A) 18 : 35 : 50
Question: For what value of x between − 9 and 9, inclusive, is the value of x^2 − 10x + 16 the greatest?
(A) − 9
(B) − 2
(C) 0
(D) 2
(E) 9
Rationale: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..
so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.
so -9 will give the greatest value..
ans A
Answer: (A) − 9
Question: If x/y = 7/4, then (x + y)/(x - y) = ?
(A) 5
(B) 11/3
(C) -1/6
(D) -1/5
(E) -5
Rationale: Any x and y satisfying x/y = 7/4 should give the same value for (x + y)/(x - y).
Say x=7 and y=4, then (x + y)/(x - y) = (7 + 4)/(7-4) = 11/3.
Answer: B.
Answer: (B) 11/3
Question: If 15% of 40 is greater than 25% of a number by 2, the number is
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Explanation:
15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16
Option B
Answer: (B) 16
Question: Mr. Hernandez, who was a resident of State X for only 12 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year?
(A)  $900
(B)  $720
(C)  $600
(D)  $300
(E)  $60
Rationale: Total tax for the year = 22,500 x 4% = 900
As stated Annual tax is prorated as per the duration of stay.
Prorated Tax = 900 (12/12) = 900
Answer A
Answer: (A)  $900
Question: Look at this series: 35, 36, 42, __, 48, 54, 35, 60, ... What number should fill the blank?
(A) 35
(B) 46
(C) 44
(D) 45
(E) 52
Rationale: A
35
In this series, 6 is added to the previous number; the number 35 is inserted as every third number.
Answer: (A) 35
Question: A number is increased by 30% and then decreased by 30%, the final value of the number is ?
(A) decreases by 7%
(B) decreases by 9%
(C) decreases by 8%
(D) decreases by 6%
(E) decreases by 5%
Rationale: Here, x = 30 and y = - 30
Therefore, the net % change in value
= ( x + y + xy/100)%
= [30 - 30 + (30 * -30)/100]% or - 9%
Since the sign is negative, there is a decrease in value by 9%.
ANSWER: B
Answer: (B) decreases by 9%
Question: The ratio of two numbers is 1 : 3 and their H.C.F. is 6. Their L.C.M. is
(A) 48
(B) 18
(C) 56
(D) 27
(E) 67
Rationale: Explanation:
Let the numbers be 1x and 5x. Then, their H.C.F. = x. So, x = 6.
So, the numbers 6 and 18.
L.C.M. of 6 and 18 = 18.
Option B
Answer: (B) 18
Question: The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
(A) A)2/3
(B) B)5/7
(C) C)4/7
(D) D)5/9
(E) E)None of these
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5n + 5 = 4(2n - 1) + 4 => n = 5/3
d = 2n - 1 => d = 3/7
Hence the fraction is : 5/7
ANSWER:B
Answer: (B) B)5/7
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 72 km downstream?
(A) 30/83 hours
(B) 33/13 hours
(C) 31/13 hours
(D) 30/13 hours
(E) 36/14 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 72 km downstream = d/s = 72/26
= 36/13 hours.
Answer:E
Answer: (E) 36/14 hours
Question: Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m. ?
(A) 72 kmph
(B) 92 kmph
(C) 12 kmph
(D) 82 kmph
(E) 14 kmph
Rationale: Explanation:
Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer: C
Answer: (C) 12 kmph
Question: If W=x^4 + y^4 = 100, then the greatest possible value of x is between
(A) 0 and 3
(B) 3 and 6
(C) 6 and 9
(D) 9 and 12
(E) 12 and 15
Rationale: My attempt:
If W=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.
Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is B
Hence answer is --
b) 3 and 6.
Answer: (B) 3 and 6
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?
(A) 7:5
(B) 7:0
(C) 7:3
(D) 7:2
(E) 7:1
Rationale: Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3.Answer:C
Answer: (C) 7:3
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 5 years the amount to be paid is?
(A) 8118
(B) 8127
(C) 8618
(D) 9125
(E) 8128
Rationale: A = 7500(26/25)5
= 9125
Answer: D
Answer: (D) 9125
Question: A man purchased 3 blankets @ Rs.100 each, 3 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 750
(B) 277
(C) 878
(D) 450
(E) 272
Rationale: 10 * 150 = 1500
3 * 100 + 3 * 150 = 750
1500 – 750= 750
Answer:A
Answer: (A) 750
Question: If P(A) = 8/15, P(B) = 4/15, and P(A âˆª B) = 16/15 Find P(B|A)
(A) 1/2
(B) 2/3
(C) 3/2
(D) 2
(E) 4/7
Rationale: P(B|A) = P(A âˆª B)/P(A)
P(B|A) = (16/15)/(8/15) = 2.
D
Answer: (D) 2
Question: Each face of a cube is painted with exactly one colour. What is the smallest number
of colours needed to paint a cube so that no two faces that share an edge are the
same colour?
(A) 2 colours
(B) 3 colours
(C) 4 colours
(D) 5 colours
(E) 6 colours
Rationale: Assume the top face of the cube is coloured green.
Since the front face of the cube shares an edge with the top face, it cannot be coloured green.
Thus, we need at least two colours.
Thus, we assume that the front face is coloured blue, as shown in Figure 1.
Since the right face shares an edge with the top face and with the front face, it cannot be
coloured green or blue. Thus, we need at least three colours.
Thus, we assume that the right face is coloured red, as shown in Figure 2.
We have shown that at least 3 colours are needed. In fact, the cube can be coloured with
exactly 3 colours by colouring the left face red, the back face blue, and the bottom face green
(Figure 3).
In this way, the cube is coloured with exactly 3 colours and no two faces that share an edge
are the same colour.
Therefore, 3 is the smallest number of colours needed to paint a cube so that no two faces that
share an edge are the same colour.which is=3
correct answer B
Answer: (B) 3 colours
Question: Virginia, Adrienne, and Dennis have taught history for a combined total of 102 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
(A)  23
(B)  32
(C)  35
(D)  43
(E)  44
Rationale: Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D
V+A+D = 96
V= A+9
=>A = V-9
V= D-9
=> A = (D-9)-9 = D-18
D-9 + D-18 + D =102
=> 3D = 102 + 27 = 129
=> D = 43
Answer D
Answer: (D)  43
Question: Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have.
(A) 16.5
(B) 17.5
(C) 18.5
(D) 19.5
(E) 20.5
Rationale: Let Siri has x Rs, then Christine has 20+x Rs
Given x + (20+x)= 21
=> 2x= 1 or x= 0.5
So Christine and Siri has 20.5 and 0.5 Rs respectively.
ANSWER:E
Answer: (E) 20.5
Question: Group A has 2 boys and 7 girls, group B has 3 boys and 4 girls and group C has 2 boys and 2 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?
(A) 312/445
(B) 105/378
(C) 291/105
(D) 209/315
(E) 77/272
Rationale: Group A has 2 boys and 7 girls; 9
Group B has 3 boys and 4 girls; 7
Group C has 2 boys and 2 girls. 4
Selected group should have one girl and two boys.
Girl from A, boy from B, boy from C: 7/9*3/7*2/4 = 1/6;
Boy from A, girl from B, boy from C: 2/9*4/7*2/4 = 4/63;
Boy from A, boy from B, girl from C: 2/9*3/7*2/4 = 3/63.
Sum = 1/6 + 4/63 + 3/63 = 105/378.
Answer: B.
Answer: (B) 105/378
Question: he number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is?
(A) 43288
(B) 2377
(C) 4320
(D) 2882
(E) 2782
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!) = 4320
Answer:C
Answer: (C) 4320
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
(A) 2277
(B) 2997
(C) 1000
(D) 2688
(E) 2677
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C
Answer: (C) 1000
Question: The radius of a cylindrical vessel is 7cm and height is 5cm. Find the whole surface of the cylinder?
(A) 281
(B) 528
(C) 440
(D) 767
(E) 1981
Rationale: r = 7 h = 5
2πr(h + r) = 2 * 22/7 * 7(12) = 528
Answer:B
Answer: (B) 528
Question: A man can row upstream at 10kmph and downstream at 14kmph. Find man's rate in still water ?
(A) 5km/hr
(B) 15km/hr
(C) 10km/hr
(D) 12km/hr
(E) 7.5km/hr
Rationale: Rate in still water = 1/2 (10+14) = 12km/hr
Answer is D
Answer: (D) 12km/hr
Question: In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket inchours, and the hot-water leak alone would fill the same bucket inhhours, wherec < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it tookthours to fill the bucket, which of the following must be true?
I. c < t < h
II. 0 < t < h
III. (c/2) < t < (h/4)
(A) a) I only
(B) b) II only
(C) c) III only
(D) d) I and II
(E) e) I and III
Rationale: I picked numbers for this problem
C = 2 hours
H = 3 hours
C<H
2 people working together formula is
1/C + 1/H = 1/t
1/2 + 1/3 = 1/t
t = 6/5 = 1.2
Substitute the values of C, H and t in the 3 choices given below
Only 2 is valid.Therefore B is the best answer
Answer: (B) b) II only
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
(A) 22 1/2 %
(B) 22%
(C) 21 %
(D) 30%
(E) 40 %
Rationale: 9 = (1*40*R)/100
R = 22 1/2 %
ANSWER A
Answer: (A) 22 1/2 %
Question: Machine E can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A)  1/2
(B)  1/3
(C)  4/13
(D)  8/29
(E)  6/33
Rationale: Let the following be true:
E makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Answer: (C)  4/13
Question: How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?
(A) 45
(B) 50
(C) 56
(D) 60
(E) 63
Rationale: Selling Price(SP) of 1 kg mixture= Rs. 9.24
Profit = 10%
Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP
=100(100+10)×9.24=100110×9.24=92.411= Rs.8.4
By rule of alligation,
CP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind
Rs. 9 Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.4 9 - 8.4 = 0.6
i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3
Suppose x
kg of kind1 sugar is mixed with 27 kg of kind2 sugar.
then x : 27 = 7 : 3
⇒3x=27×7⇒x=9×7=63
E
Answer: (E) 63
Question: It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) (2^90 - 1)
(B) (2^90 + 1)
(C) (2^96 - 1)
(D) (2^96 + 1)
(E) (2^95 + 1)
Rationale: Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
D)
Answer: (D) (2^96 + 1)
Question: Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.33 per ounce, what is the share of Arabica in this blend?
(A) 20%
(B) 24%
(C) 30%
(D) 33%
(E) 40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.4a + .3(1-a) = .33
.4a + .3 - .3a = .33
a= .3
therefore: .3/1 ounce = 30%. Therefore, the answer should be C
Answer: (C) 30%
Question: Dacid obtained 91, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 29
(B) 78
(C) 39
(D) 37
(E) 75
Rationale: Average = (91 + 65 + 82 + 67 + 85)/5
= 78
Answer: B
Answer: (B) 78
Question: The cost price of 20 books is the same as the selling price of x books. If the profit is 25%, then the value of x is?
(A) 14
(B) 16
(C) 18
(D) 22
(E) 24
Rationale: Let C.P. of each book be Re. 1 C.P. of x articles = Rs. x.
S.P. of x booksv= Rs. 20.
Profit = Rs. (20 - x).
20 - x	x 100 = 25
x
2000 - 100x = 25x
125x = 2000
x = 16.
B)
Answer: (B) 16
Question: What is the next number of the following sequence
3,5,15,75,?
(A) 1125
(B) 1200
(C) 1000
(D) 1100
(E) 1500
Rationale: 3*5=15
5*15=75
15*75=1125
therefore next no. is 1125
ANSWER:A
Answer: (A) 1125
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
(A) 729
(B) 561
(C) 456
(D) 354
(E) 163
Rationale: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans:A
Answer: (A) 729
Question: If the sum of one-half of a number exceeds one-third of that number by 7 1/3, the number is:
(A) 15
(B) 18
(C) 20
(D) 25
(E) 30
Rationale: Let the number be x. Then,
(1/2 x + 1/5 x) - 1/3 x = 22/3
11/30 x = 22/3
x = 20
ANSWER:C
Answer: (C) 20
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 1/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
(A) 9/80
(B) 3/10
(C) 261/800
(D) 35/80
(E) 497/800
Rationale: The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 3/80 = 77/80
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (77/80)(7/10) = 1 - 539/800 = 261/800
C
Answer: (C) 261/800
Question: Coins are to be put into 12 pockets so that each pocket contains at least one coin. At most 8 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
(A) 7
(B) 13
(C) 17
(D) 22
(E) 28
Rationale: Since at most 3 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1+1+1+1+1+1+1+2+3+4+5=22
Answer: D.
Answer: (D) 22
Question: The sum of n terms of a series in A.P is 6n2 + 6n. What is the 4 th term of the series?
(A) 38
(B) 49
(C) 60
(D) 48
(E) 50
Rationale: 4 th term = sum of 4 terms - sum of 3 terms
= ( 6* 42 + 6*4 ) -( 6* 32 +6*3 ), = ( 96+24 ) – ( 54+18 )
= 120 - 72 = 48
ANSWER:D
Answer: (D) 48
Question: In covering a distance of 120 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
(A) 5 km/h
(B) 8 km/h
(C) 10 km/h
(D) 15 km/h
(E) 20 km/h
Rationale: Let A's speed be X km/hr.
Then, 120/x - 120/2x = 3
6x = 120
x = 20 km/hr.
Answer : E.
Answer: (E) 20 km/h
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 11
(B) 13
(C) 55
(D) 76
(E) 81
Rationale: Explanation:
Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
\inline {\color{Blue} \left.\begin{matrix} persons &30:39 \\ working\; hours/day & 6:5 \end{matrix}\right\}::12:x}
\inline {\color{Blue} \therefore } 30 x 6 x x = 39 x 5 x 12
=> x= \inline {\color{Blue}\frac{39\times 5\times 12}{30\times 6}}
=> x= 13
Answer: B
Answer: (B) 13
Question: How many seconds does Sandy take to cover a distance of 600 meters, if Sandy runs at a speed of 15 km/hr?
(A) 128
(B) 136
(C) 144
(D) 152
(E) 160
Rationale: 15 km/hr = 15000 m / 3600 s = (150 / 36) m/s = (25 / 6) m/s
time = 600 / (25/6) = 144 seconds
The answer is C.
Answer: (C) 144
Question: How many different subsets of the set {10, 14, 15, 24} are there that contain an odd number of elements?
(A)  8
(B)  6
(C)  18
(D)  10
(E)  12
Rationale: Answer = A = 8
{10}
{14}
{15}
{24}
{10, 14, 15}
{14, 15, 24}
{10, 15, 24}
{10, 14, 24}
Answer: (A)  8
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
(A) 32.6
(B) 32.4
(C) 32.9
(D) 32.2
(E) 32.1
Rationale: 36/7 r = 6.3 = 32.4
Answer:B
Answer: (B) 32.4
Question: From a group of boys and girls, 15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning?
(A) 40
(B) 30
(C) 50
(D) 60
(E) 10
Rationale: Let at present there be x boys.
Then,no of girls at present=5x
Before the boys had left:no of boys=x+45
And no of girls=5x
X+45=2*5x
9x=45
x=5
no of girls in the beginning=25+15=40
Answer is A.
Answer: (A) 40
Question: Find the average of first 10 natural numbers.
(A) 20.5
(B) 18
(C) 19.5
(D) 19
(E) 5.5
Rationale: Exp. Sum of first n natural numbers = n( n+1)/2
So, sum of first 10 natural numbers = 10*11/2 = 55
Required average =55/10 =5.5
Answer:E
Answer: (E) 5.5
Question: Two partners in a business (Miles and King) invested $1200 and $2000 in a business respectively. At the end of the year they made a profit of $1500. Find share of each partner?
(A) $562.5,$677.5
(B) $555.5,$937.5
(C) $562.5,$939.5
(D) $662.5,$937.5
(E) $562.5,$937.5
Rationale: A:B = 1200:2000
A:B = 3 : 5
A's share = 1500*3/8 = $562.5
B's share = 1500*5/8 = $937.5
Answer is E
Answer: (E) $562.5,$937.5