MU-NLPC/Calc-aqua_rat huggingface dataset:
Two family reunions are happening at the Park Avenue hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 70 people attend the Hall reunion, how many people attend both reunions Options.
A) 2  B) 5  C) 10  D) 16  E) 22

Solution: No of people in Oates reunion=40   No of people in Hall reunion=70   Attending both=x   All guests attend at least one.   Therefore, 100=40+70-(Both)   Both=10   Answer 10
Answer: C
Sony and Johnny caught 75 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch? Choose the correct choice from the following answers.
A) 12
B) 16
C) 34
D) 38
E) 15

Solution: s+j=75   s=4*j   j=15   ANSW15R:15
Answer: E
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:	Options.
A) 52:59  B) 52:53  C) 52:51  D) 52:52  E) 52:58

Solution: Explanation:   Let C.P. of the article be Rs. x.   Then, required ratio = 104% of x / 106% of x   = 104/106 = 52/53 = 52:53   Answer: 52:53
Answer: B
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done? Choose the correct choice from the following answers:
A) 650	B) 656	C) 756	D) 760	E) 780

Solution: From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.   Hence we have the following 3 options.   We can select 5 men ...(option 1)   Number of ways to do this = 77565   We can select 4 men and 1 woman ...(option 2)   Number of ways to do this = 77564 × 67561   We can select 3 men and 2 women ...(option 3)   Number of ways to do this = 77563 × 67562   Total number of ways   = 77565 + (77564 × 67561) + (77563 × 67562)   = 77562 + (77563 × 67561) + (77563 × 67562)[∵ n756r = n756(n - r) ]   =   7   ×   6   2   ×   1   +   7   ×   6   ×   5   3   ×   2   ×   1   ×   6   =7×62×1+7×6×53×2×1×6   +   7   ×   6   ×   5   3   ×   2   ×   1   ×   6   ×   5   2   ×   1   +7×6×53×2×1×6×52×1   =   21   +   210   +   525   =756   756)
Answer: C
If 5 (A's capital) = 10 (B's capital) = 15 (C's capital). Then the ratio of their capitals is? Choose the correct choice from the following answers: A) 5:3:2 B) 7:3:2 C) 6:3:3 D) 6:3:2 E) 5:3:2

Solution: 5A = 10B = 15 C   A:B:C = 1/5:1/10:1/15   = 6:3:2   Answer: 6:3:2
Answer: D
How many ways are there to arrange the letters in the word Teressa ?  Choose the correct choice from the following answers:
A) 1
B) 1260
C) 3780
D) 7560
E) 11340

Solution: 7 total words, 2E, 2S   = 7! / 2 ! * 2! = 1260. Answer 1260
Answer: B
The expression 10^13−120 is divisible by all of the following integers EXCEPT	Select the correct option:
A) 2	B) 13	C) 4	D) 8	E) 11

Solution: Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (B) is correct. 13
Answer: B
Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?	Choose the most appropriate option:
A) 55/228
B) 55/228
C) 55/221
D) 55/212
E) 55/2234

Solution: We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.   Let A = event of getting both black cards   B = event of getting both queens   A∩B = event of getting queen of black cards   n(A) = \inline {\color{Black}2655/221_{2}} = = 325, n(B)= \inline {\color{Black}455/221_{2}} = = 6 and n(A∩B) = \inline {\color{Black}255/221_{2}} = 1   P(A) = n(A)/n(S) = 325/1326;   P(B) = n(B)/n(S) = 6/1326 and   P(A∩B) = n(A∩B)/n(S) = 1/1326   P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 = 55/221   Answer: 55/221
Answer: C
A, B and C enter into a partnership. They invest Rs. 80,000, 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? Pick one
A) 2 : 3 : 4	B) 3 : 2 : 4	C) 6 : 2 : 1	D) 6 : 4 : 7	E) none

Solution: Sol.   A : B : C = (80000 * 36) : (80000 * 12 + 40000 * 24)   : (120000 * 24 + 40000 * 12) =288 : 192 : 336 = 6: 4 : 7   Answer 6 : 4 : 7
Answer: D
. Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?	Choose the correct choice from the following:
A) 540  B) 300  C) 890  D) 750  E) 460

Solution: 540+B+C = 1170   4540 = 3B = 2C = x   540:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1170 = Rs.540   540NSWER 540
Answer: A
Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61
Choose the correct choice.
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Given Expression = a(power 2) - b(power 2) / a-b   = (a + b)(a - b) / (a-b)   = (a + b) = (2.39 + 1.61)= 
(2.39 + 1.61) = 4
4.   4nswer is 4.
Answer: A
If x+|x|+y=4 and x+|y|-y=3 what is x+y=?	Pick one:
A) 1 B) -1 C) 3 D) 5 E) 13

Solution: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.   If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).   Answer: C.   Adding both eqn we get 2x +IxI+IyI = 13   Now considering X <0 and y>0   2x-x +y = 13   we get x+y =3   Hence answer should be 3
Answer: C
What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 757.48 = 443.095 + ?
Pick:
A) 870
B) 790
C) 680
D) 770
E) 890

Solution: ? = 285 + 1895 – 755 – 745 or, ? = 680   Answer 680
Answer: C
If 522x is a 3 digit no. with as a digit x. If the no.is divisible by 6, What is the value of the digit x is?
Choose the correct choice from the following choices:
A) 1
B) 6
C) 4
D) 7
E) 9

Solution: If a number is divisible by 6 , it must be divisible by both 2 and 3   In 522x, to this number be divisible by 2, the value of x must be even. So it can be 2,4 or 6 from given options   552x is divisible by 3, If sum of its digits is a multiple of 3.   5+5+2+x =12+x ,   If put x =2 , 12+2=14 not a multiple of 3   If put x =4 , 12+6=18 is a multiple of 3   If put x =6 , 12+2=14 not a multiple of 3   The value of x is 6.   6
Answer: B
4 points are marked on a straight line and another 5 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? Pick:	A) 91	B) 105	C) 196	D) 2	E) 14

Solution: assuming that the top line can have either 2 points or 1 point...   4! / 1!3! - 4! / 2! 2! yields 2.   2
Answer: D
56, 63, 59, 11, 57, 6, 11
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
Choose the correct answer:
A) 21
B) 32
C) 49
D) 56
E) 58

Solution: Yes, it can be solved with observation even without approximation in 30 sec.   Just observe given numbers: 6,11 ,11, 56, 57, 59,63   Median is very easy to tell - its 56. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 56? DE are already out.   Now, we have 21, 32 and 49 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 49. (Notice, if 21 is more than mean then 49 is also. If 32 is more than mean, 49 is also. )   Hence 49 it is!
Answer: C
Based on this year's costs, a factory budgets P dollars for planing N new cars next year. If the average cost of building each car were to increase 50% from this year's cost, then the greatest number of cars that the factory could build next year using P dollars would be:
Choose the correct choice from the following:
A) 33% less than N
B) 67% less than N
C) Equal to N
D) 33% greater than N
E) 67% greater than N

Solution: Correct answer is (A).   This year, the price of a car is price1=P/N.   If this price increases by 50% it becomes Price2=P/N*1.5   Then with P dollars, you can build P/Price2 cars i.e. P/(P/N*1.5) i.e. N/1.5 i.e. 0.67*N   Which is 33% less than N.
Answer: A
A and B walk around a circular track. A and B walk at a speed of 4 rounds per hour and 5 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 10.30 a.m.?  Choose the correct choice from the following answers
A) 10	B) 20	C) 22	D) 9	E) 5

Solution: Relative speed = Speed of A + Speed of B (âˆ´ they walk in opposite directions)   = 4 + 5= 
4 + 5 = 9
9 rounds per hour=> They cross each other 9 times in 1 hour and 4 times in 1/2 hour   Time duration from 8 am to 10.30 am =2.5 hour   Hence they cross each other 22 times before 10.30 am   Answer : 22
Answer: C
The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 13 days, how large is the colony today? Choose the correct choice from the following:	A) 512	B) 1024	C) 768	D) 2048	E) 4096

Solution: 9 days ago- 2   8 days ago- 4   7 days ago- 8   6 days ago- 16   5 days ago- 32   4 days ago- 64   3 days ago- 128   2 days ago- 256   Yesterday- 512   Today- 1024   Ans:1024
Answer: B
In a certain pond, 35 fish were caught, tagged, and returned to the pond. A few days later, 35 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond? Answers.
A) 400
B) 625
C) 875
D) 2500
E) 10 000

Solution: If x is total number of fish in the pond :   4 = 35/x * 100   => x = 875   So answer is 875
Answer: C
What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it?
Choose the correct choice from the following answers
A) 600  B) 602  C) 604  D) 606  E) 608

Solution: The nth term is 2+3*(n-1).   The 201st term is 2 + 3(200) = 602   The answer is 602.
Answer: B
For all integers a and b, a%b = (a + b)(a - b). If 6%x = 11, then which of the following could be a value of x?  Choose the correct choice from the following:
A) -5
B) -3
C) 2
D) 3
E) 6

Solution: 6%x = (6+x)(6-x)   36-x^2 = 11   x^2 = 25   x=-5,5   -5ns: -5
Answer: A
If two projectiles are launched at the same moment from 1182 km apart and travel directly towards each other at 460 km per hour and 525 km per hour respectively, how many minutes will it take for them to meet?
Answers.
A) 68
B) 72
C) 76
D) 80
E) 84

Solution: The projectiles travel a total of 985 km per hour.   The time to meet is   1182/985= 
  1182/985 = 6/5 = around 1.2
1.2 hours= 72 minutes   The answer is 72.
Answer: B
In how many different ways can the letters of the word "CLAIM" be rearrangement?	Pick one:
A) 100	B) 120	C) 140	D) 150	E) 160

Solution: The total number of arrangements is   5P5 = 5! = 120   120)
Answer: B
The length of a rectangle is three times of its width. If the length of the diagonal is 8√10 then find the perimeter of the rectangle.
Answers
A) 77 cm	B) 88 cm	C) 64 cm	D) 11 cm	E) 18 cm

Solution: Let Breadth = x cm,   then, Length = 3x cm   x2+(3x)2=(810−−√)2=>10x2=640=>x=8   x2+(3x)2=(810)2=>10x2=640=>x=8   So, length = 24 cm and breadth = 8 cm   Perimeter = 2(l+b)   = 2(24+8) = 64 cm   Answer:64 cm
Answer: C
The music class consists of 4 girls and 8 boys. How many ways can a group of 3 be formed if it has to include at least one boy?	Select:
A) 155
B) 158
C) 161
D) 165
E) 216

Solution: Reverse combinatorics approach is preferred method on this one   Note that at least 1 boy gives clue to using this method   All combinations - four girls = answer   All combinations is 12C3 = 220   All girls 4C3 = 4   So our answer is   220-4= 
  220-4 = 216
216   Hence, answer is (216)
Answer: E
The average (arithmetic mean) monthly income of four workers is $2,600. After one worker’s income increases by 20 percent the new average income is $2,800. What was the original income of the worker whose monthly income increased?
Choose the most appropriate option: A) $4,000 B) $4,500 C) $4,100 D) $4,300 E) $5,000

Solution: Increase in total income was 200*4= 
200*4 = 800
$800, we know that this increase was 20% (1/5th) of the workers original income, thus his/her original income was 800*5=$4,000.   $4,000nswer: $4,000
Answer: A
Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Pick
A) 11 1/2 min
B) 11 1/4 min
C) 11 2/4 min
D) 11 1/5 min
E) 11 7/4 min

Solution: 3/12 + x/15 = 1   x= 11 1/4   Answer: 11 1/4 min
Answer: B
On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
Choose the correct option
A) 10 B) 12 C) 14 D) 16 E) 17

Solution: d = (D-R)/Q   = (109 - 1)/9   = 108/9= 
108/9 = 12
12   12
Answer: B
Which of the following CANNOT be weighed using a balance scale and these unit weights: 2, 4, 7, and 10  Choose one
A) 16  B) 15  C) 18  D) 19  E) 21

Solution: A. 13 (can be weighed by keeping weights of 10, 2 and 4 )   B. 15 (cannot be weighed)   C. 17 (can be weighed by keeping weights of 10 and 7 kg)   D. 19(can be weighed by keeping weights of 10, 2 and 7 kg)   E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)   15
Answer: B
If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Select the correct option:
A) 118 km  B) 162 km  C) 1767 km  D) 1887 km  E) 177 km

Solution: 12 m/s = 12 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 12 * 18/5 * 15/4= 
12 * 18/5 * 15/4 = 162
162 km.   Answer: 162 km
Answer: B
Bill is golfing with three friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 10 golf tees for each member of his foursome, if he will buy no more than 3 packages of the generic golf tees?	Choose the most appropriate option.
A) 16
B) 10
C) 8
D) 4
E) 2

Solution: At least 10 golf tees for each member of his foursome = total of at least 4*10= 
4*10 = 40
40 tees.   3 packages of the generic golf tees, that are packaged by the dozen= 3*12= 
3*12 = 36
36 tees.   So, Bill must by at least 16 Aero tees. They come by the pair, hence he must by at least 4/2= 
4/2 = 2
2 packages of Aero flight tees.   Answer: 2.
Answer: E
A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Choose the correct choice from the following answers:
A) 27  B) 76  C) 82  D) 80  E) 23

Solution: Given M + P + C = 80 * 3= 
80 * 3 = 240
240 --- (1)   M + P= 90 * 2= 
90 * 2 = 180
180 --- (2)   P + C= 70 * 2= 
70 * 2 = 140
140 --- (3)   Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.   P= (2) + (3) - (1) = 180 + 140 - 240= 
180 + 140 - 240 = 80
80   Answer:80
Answer: D
Jack splits his bucket of apples into 5 groups of equal size, but has 2 left over. The next day, he repeats the process with a bucket that contains exactly 3 times as many apples as the day before. How many does he have left over this time?	Choose the correct choice from the following:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: Set x = to number of apples in his basket, and y to be the number of apples per group.   x = 5*y +2.   3x = 15*y+6   3x = 3*5*y + 6   3x = 5(3(y+1))+1   Remainder is then 1, so option 1.
Answer: B
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 9 m x 6 m x 22.5 cm? Choose the correct choice:
A) 6400
B) 6410
C) 6440
D) 7200
E) 6800

Solution: Number of bricks = Volume of Wall/Volume of Bricks   =900x600x22.5/25x11.25x6= = 7200   answer :7200
Answer: D
The price of sugar is increased by 8%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
Choose one:
A) (800/108) %	B) (107/100) %	C) (100/107)%	D) (7/100)%	E) (100/700)%

Solution: Old price = $100 (assume);   Old consumption = 1 kg (assume).   New price = $108.   We want the spendings to remain at $100.   (New consumption)*108 = 100 --> (New consumption) = 100/108 kg.   Percent decrease = Change/Original *100 = (1 - 100/108)/1*100 = 800/108%.   (800/108) %nswer: (800/108) %.
Answer: A
Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 15%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?	Select the correct option.
A) $146.6 B) $120 C) $180 D) $220 E) $260

Solution: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.   $146.6-E = 1/12*($146.6+E) ==> 11$146.6 = 13E ------------ (1)   Second condition gives two different amounts, $146.6l's amount = 1.1$146.6 and Eliot's amount = 1.2E   1.1$146.6 = 22 + 1.15E ==> 11$146.6 =220 +11.5E -------(2)   Substituting (1) in (2):   13E = 220+11.5E ==>1.5E= 220 or E =440/3 =146.6   $146.6
Answer: A
Eleven books consisting of 2 financial management, 4 marketing management and 5 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.	Choose the correct choice:	A) 1/1455	B) 1/1355	C) 1/2255	D) 1/1155	E) 1/5040

Solution: Since the denominator will be 11! . And there is no way to divide 11 from numerator and denominator. Use a multiple of 11 in the denominator only answer   1/1155
Answer: D
P and Q invested in a business. The profit earned was divided in the ratio 3 : 5. If P invested Rs 12000, the amount invested by Q is  Choose the correct choice from the following choices:
A) 30000 B) 50000 C) 40000 D) 20000 E) 60000

Solution: Let the amount invested by Q = q   12000:q=3:5   ⇒12000×5=3q   ⇒q=(12000×5)/3=30000   30000nswer is 30000
Answer: A
A single discount equivalent to the discount series of 20%, 10% and 8% is?
Choose the most appropriate option.
A) 31.6 B) 31.0 C) 31.6 D) 31.1 E) 33.76

Solution: 100*(80/100)*(90/100)*(92/100)   = 68.4   100 - 66.24= 
100 - 66.24 = 33.76
33.76   Answer: 33.76
Answer: E
If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
Answers
A) 1 hour
B) 2 hour
C) 3 hour
D) 4 hour
E) 5 hour

Solution: Speed Ratio = 1:3/4 = 4:3   Time Ratio = 3:4   1 -------- 1/3   3 --------- ? è 1 hour   Option 1 hour
Answer: A
What is the value of (P + Q)/(P - Q) if P/Q is 6?  Pick one
A) 4/3  B) 2/3  C) 2/6  D) 7/5  E) 8/7

Solution: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]   = (6 + 1)/(6 - 1)   = 7/5   ANSWER:7/5
Answer: D
Two brothers took the GMAT exam, the higher score is R and the lower one is S. If the difference between the two scores is equal to their average, what is the value of S/R ?
Choices:
A) 3 B) 2 C) 1/2 D) 1/3 E) There isn't enough data to answer the question.

Solution: Answer is 1/3 : 1/3   R - S = (R + S)/2   Solving for S/R = 1/3   1/3
Answer: D
If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 1
II. -1
III. 2  Pick:
A) II only B) III only C) I and II only D) II and III only E) I and III only

Solution: Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.   n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.   It can be 1 for n=2 and 2 for n=5.   Answer: I and III only.
Answer: E
If x and y are integers and x + y = 8, which of the following must be true?	Choose the correct answer
A) x and y are consecutive integers.	B) Both x and y are even.	C) If x > 0, then y < 0.	D) If x < 0, then y > 0.	E) Both x and y are less than 5.

Solution: In option C if x > 0,then y<0 means x is +ve and y is -ve   In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.   How option If x < 0, then y > 0. is right could you explain
Answer: D
The probability is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least o ne of the tosses will turn up tails?	Select the correct option:
A) 0.064  B) 0.36  C) 0.64  D) 0.784  E) 0.936

Solution: probability that at least one of the tosses will turn up tails = 1 - probability that all will be heads   = 1 - (0.4*0.4*0.4)   = 1 - 0.064= 
1 - 0.064 = 0.936
0.936 0.936
Answer: E
if 4y = 12x + 20,4x + 2y = 20 ,what is the value of y? Choose the most appropriate option:
A) 8.5 B) 6 C) 7 D) 8 E) 9

Solution: solution:   I---> y = 3x + 5   sub in II   4x + 2(3x + 5) = 20   10x = 10   x = 1   sub x=1 in other equation   4y = 12(1) + 20   y = 8   answer is 8
Answer: D
The radius of a wheel is 20 cm. What is the distance covered by the wheel in making 500 resolutions?  Choose the correct answer.
A) 708 m
B) 704 m
C) 314.3 m
D) 714 m
E) 744 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 20 = 31428.5 cm   = 314.3 m   Answer:314.3 m
Answer: C
Half of 4 percent written as decimal is
Choose the most appropriate option:  A) 0.02  B) 0.5  C) 0.05  D) 0.005  E) None of these

Solution: Explanation:   It will be 1/2(4%) = 1/2(4/100) = 4/200= 
4/200 = 1/50 = around 0.02
0.02   0.02nswer: Option 0.02
Answer: A
The pages of a report are numbered consecutively from 1 to 6. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =  Choose the correct choice from the following options.
A) 4	B) 5	C) 6	D) 3	E) 2

Solution: sum of the first few numbers =1+2+3+4= 
1+2+3+4 = 10
10   sum of the last few= 5 +6= 
5 +6 = 11
11 page no.4 answer .4
Answer: A
Kelvin earns $60 a week from his job. His income increased and now makes $70 a week. What is the percent increase?
Choose the correct choice from the following choices.
A) 16.66%  B) 20%  C) 22.5%  D) 23%  E) 24.5%

Solution: Increase = (10/60)*100 = (1/6)*100 = 16.66%.   16.66%
Answer: A
Suraj has a certain average of runs for 16 innings. In the 17th innings he scores 112 runs thereby increasing his average by 6 runs. What is his average after the 17th innings?	Pick.
A) 18 B) 25 C) 16 D) 72 E) 27

Solution: To improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings.   Thus, the average after the 17th innings   = 112 - 96= 
112 - 96 = 16
16.   ANSWER:16
Answer: C
In a group of ducks and cows, the total number of legs are 8 more than twice the no. of heads. Find the total no.of buffaloes.  Choose the correct option.
A) 5  B) 4  C) 6  D) 3  E) 2

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 8   => 2x = 8 => x = 4   4
Answer: B
Agnes has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?  Choose the most appropriate option.
A) 32
B) 30
C) 29
D) 28
E) 27

Solution: 5v + 10y = 460   v > y   Pick an easy number to work with.   suppose v=30.   Then you have 150.   You need another 310 and that means you need y=31 which is greater than v.   Therefore, v > 30.   The only answer choice where v > 30 is if v = 32.   32 is the answer.
Answer: A
If a positive integer n is divisible by both 3 and 5, then n must also be divisible by which of the following?
I. 15
II. 8
III. 45  Options:
A) None
B) I only
C) II only
D) I and II
E) II and III

Solution: A multiple of 3 and 5 is also a multiple of 15, but not necessarily a multiple of 8 or 45.   The answer is I only.
Answer: B