MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the greatest value of n such that 17^n is a factor of 17! ?
Options
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Another way to solve this question :   We know that 18 = 2 *3^2.   Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)   No. of 3s = 18/3= 
18/3 = 6
6/3= 
6/3 = 2
2.   Add the numbers in Bold, you will get total number of 3s= 8.   Hence, total number of 2^2 = 4/2= 
4/2 = 2
2.   Hence, answer is 2. 2
Answer: B
What is the area of square field whose side of length 20 m? Choose the correct option:
A) 200 sq m  B) 186 sq m  C) 586 sq m  D) 287 sq m  E) 400 sq m

Solution: 20 * 20= 
20 * 20 = 400
400 sq m   Answer: 400 sq m
Answer: E
In the biology lab of "Jefferson" High School there are 2.16*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
Choose the correct choice from the following choices:	A) 100	B) 200	C) 500	D) 1000	E) 5000

Solution: 2.16*10^6/ 10800==> 21.6*10^3/108==> 21600/108= 
21600/108 = 200
200   ANSWER:200
Answer: B
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?	Choose the correct choice from the following
A) 3/8
B) 3/2
C) 3/5
D) 3/9
E) 3/1

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train   = 17 y meters. (27 x + 17 y) / (x + y)   = 23 ==> 27 x + 17 y   = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2   Answer: 3/2:
Answer: B
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?	Pick one:
A) 6.24 km  B) 6 km  C) 5.76 km  D) 5.66 km  E) 10 km

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   ANSWER:5.76 km
Answer: C
A profit of Rs. 900 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
Choose the correct choice from the following answers
A) s. 280  B) s. 180  C) s. 380  D) s. 50  E) s. 90

Solution: A profit of Rs. 900 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.   so profits are 540 and 360.   difference in profit share = 540-360= 
540-360 = 180
180   ANSWER:s. 180
Answer: B
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? Choose the correct choice from the following answers
A) 155 m
B) 150 m
C) 187 m
D) 177 m
E) 186 m

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y   = x/15   (x + 100)/25   = x/15   => x = 150 m.   Answer: 150 m
Answer: B
What will come in place of the x in the following Number series? 6, 12, 21, x , 48	Answers.
A) 33 B) 36 C) 45 D) 50 E) 52

Solution: (A)   The pattern is + 6, + 9, + 12, +15 ………..   So the missing term is = 21 + 12= 
21 + 12 = 33
33
Answer: A
An investor bought two shares of stock, which he sold for $48 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:	Pick one:
A) a profit of $10
B) a profit of $4
C) a loss of $4
D) a loss of $10
E) neither a profit nor a loss

Solution: The cost of the first stock was 48/1.2= 
48/1.2 = 40
40, so the profit from it is 8.   The cost of the second stock was 48/0.8= 
48/0.8 = 60
60, so loss from it is 12.   Overall the loss is $4.   The answer is a loss of $4.
Answer: C
How many times are the hands of a clock at right angle in a day?
Select the correct option.
A) 22	B) 24	C) 44	D) 46	E) 48

Solution: In 12 hours, they are at right angles 22 times.   In 24 hours, they are at right angles 44 times. Answer: Option 44
Answer: C
What is the remainder when (63)(65) is divided by 8?	Pick one
A) 1
B) 2
C) 4
D) 5
E) 7

Solution: (63)(65) = (64-1)(64+1) = 64^2 - 1 which is 1 less than a multiple of 8.   Then the remainder will be 7.   The answer is 7.
Answer: E
Tara bought 19 cartons of ice cream and 4 cartons of yoghurt. Each carton of ice cream cost $7 and each carton of yoghurt cost $1. How much more did Tara spend on ice cream than on yoghurt?  Choose the correct choice from the following answers:
A) $144	B) $130	C) $80	D) $110	E) $129

Solution: Step 1: Find the cost of the ice cream.   19 × $7 = $133   Step 2: Find the cost of the yoghurt.   4 × $1 = $4   Step 3: Find how much more the ice cream cost than the yoghurt.   $133 – $4 = $129   Tara spent $129 more on ice cream.   Answer is $129.
Answer: E
If k and w are the dimensions of a rectangle that has area 21, and if k and w are integers such that k > w, what is the total number of possible values of k?
Answers:  A) Two  B) Three  C) Four  D) Five  E) Six

Solution: kw=21=21*1=7*3--> k can take 2 values,   Twonswer: Two
Answer: A
Find the invalid no.from the following series 2,3,12,37,86,166,288 Choose the correct answer.
A) 2 B) 3 C) 166 D) 37 E) 86

Solution: 3-2= 
3-2 = 1
1   12-3= 
12-3 = 9
9   37-12= 
37-12 = 25
25   86-37= 
86-37 = 49
49   166-86= 
166-86 = 80
80(this must be 81=167-86= 
167-86 = 81
81)   so wrong number in the sequence is 166   difference between two sucessive numbers sequence would be   1,9,25,49,81,121(square of 1,3,5,7,9,11)   166
Answer: C
An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 20 gallons of ethanol, how many gallons of fuel A were added? Choose one:  A) 300  B) 150  C) 100  D) 80  E) 50

Solution: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.   The amount of ethanol in A gallons of fuel A is 0.12A;   The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);   Since the total amount of ethanol is 20 gallons then 0.12A+0.16(200-A)=20 --> A=300.   300nswer: 300.
Answer: A
When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction e of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
Pick one.
A) 11/14
B) 13/18
C) 4/7
D) 3/7
E) 3/14

Solution: If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.   2/9 of the votes on a certain resolution have been counted--> 4 counted and  18-4= 
 18-4 = 14
14 votes left to be counted;   3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;   Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of   18*2/3= 
  18*2/3 = 12
12 people who voted against, so in the remaining 14 votes there should be   12-1= 
  12-1 = 11
11 people who voted against. Thus e=11/14 of the remaining votes must be against.   11/14nswer: 11/14.
Answer: A
Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 18 boys and 42 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad? Choose one.
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.   Table method is shown above; here is how you will use logic:   There are 6 happy boys.   There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.   We have 6 happy boys and 6 sad boys. Total we have 18 boys. So  18 - 6 - 6= 
 18 - 6 - 6 = 6
6 boys must be neither happy nor sad.   Answer (6)
Answer: C
A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream. Select the correct option.
A) 2	B) 2.5	C) 1.5	D) 1	E) 3

Solution: Speed - x   upward speed (4.5-x)   downward = 4.5+x   distance => y   time rowing upwards = 2 * time rowing upwards   y/4.5-x = 2*y/4.5+x   x =1.5 km/hr   ANSWER 1.5
Answer: C
Which of the following is closest to (7!-6!)/(7!+6!)?	Choose the correct option:
A) 0.75 B) 1.25 C) 0.92 D) 0.86 E) 1

Solution: (7!-6!)/(7!+6!)   6! (7-1)/6! (7+1)   6/8 = 3/4= 
3/4 = 3/4 = around 0.75
0.75   0.75 is the answer
Answer: A
Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?	Choose the correct answer
A) 10 B) 12 C) 14 D) 17 E) 18

Solution: Let the numbers be x, x+2 and x+4 then   x + x+2 + x+4 = x+26   3x + 6 = x + 26   2x = 20   \inline \therefore x = 10   \inline \therefore Middle number = x + 2 = 10+2= 
10+2 = 12
12   12
Answer: B
One year ago the ratio between Laxman's and Gopal's salary was 3:4. The ratio's of their individual salaries between last year's and this year's salaries are 4:5 and 2:3 respectively. At present the total of their salary is Rs.4290. The salary of Laxman now is :  Choose the most appropriate option: A) Rs.1040 B) Rs.1650 C) Rs.2560 D) Rs.3120 E) None

Solution: Explanation:   Let the salaries of Laxman and Gopal one yer before be 12x and 16x.   Given that laxman's last year and present year salary are in the ratio 4 : 5 so his present salary = 5/4(12x) = 15x   Also Gopal's last year and present year salary are in the ratio 2 : 3 so his present salary = 3/2(16x) = 24x   Rs.1650ut given that sum of the salaries 15x + 24x = 39x  15  + 24= 
 15  + 24 = 39
39x= 4290 ⇒⇒ x = 110   Laxman's present salary = 15x = 15 x 110 = 1650   Correct Option: Rs.1650
Answer: B
The distance between 2 cities A and B is 1000km. A train starts from A at 9 a.m. and travels towards B at 100 km/hr. Another starts from B at 10 a.m. and travels towards A at 150 km/hr. At what time do they meet? Select:
A) 11am.
B) 12p.m.
C) 3pm.
D) 2p.m.
E) 1p.m.

Solution: Suppose they meet x hrs after 9 a.m.   Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000   100x + 150 (x-1) = 1000   x = 4.60 = 5 hrs   They meet at 9+5 = 2 p.m.   Answer is 2p.m.
Answer: D
To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?  Choose the correct answer:
A) Combined, with a saving of 5 cents	B) Combined, with a saving of 10 cents	C) Combined, with a saving of 15 cents	D) Separately, with a saving of 5 cents	E) Separately, with a saving of 10 cents

Solution: 3 pounds cost = 10+2*5= 
10+2*5 = 20
20   5 pounds cost= 10+4*5= 
10+4*5 = 30
30   Total= 50   8 pounds cost = 10+ 7*5= 
10+ 7*5 = 45
45   Combined, with a saving of 5 centsnswer : Combined, with a saving of 5 cents
Answer: A
From the given equation find the value of z: zÂ² + 5z + 6 Options
A) 2 B) 1 C) -1 D) -3 E) 3

Solution: (z + 2)(z + 3)   Z = -2 or -3   Answer is -3
Answer: D
A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values Z are within three standard deviations of the mean?	Select:
A) 0	B) 1	C) 3	D) 6	E) 7

Solution: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.   With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range. 1
Answer: B
In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is  Choose the most appropriate option
A) 35
B) 37
C) 39
D) 41
E) 42

Solution: Explanation:   Let B's age = x years.   Then, As age = (x+ 9) years.   (x+9+10)=2(x—10)   hence x=39.   Present age of B = 39 years   Answer: Option 39
Answer: C
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent Z of all the people in Smithtown are left-handed women?
Select:
A) 50%  B) 40%  C) 25%  D) 20%  E) 10%

Solution: looking at the ratio we can take total number of people=20..   ans 5/20 or 25% 25%
Answer: C
The average age of 11 boys is 50, if the average age of first six boys is 49 and that of the last six is 52. Find the boy age?	Choose the correct option.
A) 48  B) 50  C) 56  D) 62  E) 64

Solution: 1 to 11 = 11 * 50= 
11 * 50 = 550
550   1 to 6= 6 * 49= 
6 * 49 = 294
294   6 to 11= 6 * 52= 
6 * 52 = 312
312   6th= 294 + 312 – 550 = 56   56
Answer: C
in how many ways can six members be selected from a group of ten members? Choose the correct choice from the following:
A) 10C6
B) 10C4
C) 10C9
D) 10C2
E) 10C1

Solution: Six members can be selected from ten members in   10C6 = 10C4 ways.   Answer: 10C4
Answer: B
A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 220 square feet and its length is 12 feet longer than its width. If the uniform width between the rug and room is 12 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?	Choose the correct choice from the following
A) 32  B) 1136  C) 40  D) 1344  E) 104

Solution: Rug's area = 220   which is (x) x (12+x) = 220   so x= 10   rug maintains a uniform distance of 12 feet   so room has dimension 10+24 and 22+24 i.e. 34 and 46   area of room 34x46 = 1564   area covered is 120   so uncovered area is 1564-220= 
1564-220 = 1_344
1344 (ANSWER 1344)
Answer: D
A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?	Options:	A) 288	B) 121	C) 772	D) 992	E) 212

Solution: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]   = [1600 * 41/40(41/40 + 1)   = [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.   C.I. = 3321 - 3200 = Rs. 121.   Answer: 121
Answer: B
If x + (1/x) = 5, what is the value of T= x^2 + (1/x)^2?  Select the correct option: A) T=21 B) T=22 C) T=23 D) 24 E) 27

Solution: Squaring on both sides,   x^2 + (1/x)^2 + 2(x)(1/x) = 5^2   x^2 + (1/x)^2 = 23   Answer: T=23
Answer: C
In how many ways can an answer key for a quiz be written if the quiz contains 4 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?	Choose the correct choice from the following choices.
A) 120	B) 190	C) 224	D) 298	E) 256

Solution: There are 2^4 = 16 possibilities for the true-false answers.   However we need to remove two cases for TTTT and FFFF.   There are  4*4= 
 4*4 = 16
16 possibilities for the multiple choice questions.   The total number of possibilities is  14*16= 
 14*16 = 224
224.   The answer is 224.
Answer: C
In a class of 94 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?  Answers:
A) 6
B) 15
C) 24
D) 33
E) 40

Solution: Formula for calculating two overlapping sets:   A + B - both + NOT(A or B) = Total   so in our task we have equation:   41 (french) + 22 (german) - 9 (both) + NOT = 94   54 + NOT = 94   NOT = 94 - 54= 
94 - 54 = 40
40   So answer is 40
Answer: E
If the product of two positive integers is 50, which of the following could be the LCM and HCF of the two numbers?
1. LCM 10 : HCF 5
2. LCM 25 : HCF 2
3. LCM 18 : HCF 4  Choose the correct choice
A) II only
B) I only
C) III only
D) II,III only
E) I,III only

Solution: Answer : I only
Answer: B
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.  Choices.
A) 28 kmph  B) 26 kmph  C) 24 kmph  D) 84 kmph  E) 74 kmph

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 3x/(x/8)   = 24 kmph   Answer:24 kmph
Answer: C
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4. If the project took 90 hours, how many more hours did the hardest working person work than the person who worked the least?
Choose the correct choice from the following choices
A) 18 hours B) 22 hours C) 25 hours D) 26 hours E) 20 hours

Solution: Let the persons be A, B, C.   Hours worked:   A = 2*90/9= 
2*90/9 = 20
20 hours   B= 3*90/9= 
3*90/9 = 30
30 hours   C= 4*90/9= 
4*90/9 = 40
40 hours   C is the hardest worker and A worked for the least number of hours. So the difference is  40-20= 
 40-20 = 20
20 hours.   Answer : 20 hours
Answer: E
Find the quotient: 0.63 / 9
Select the correct option:
A) 0.5 B) 0.3 C) 0.9 D) 0.1 E) 0.7

Solution: 63 / 9= 
63 / 9 = 7
7. Dividend contains 2 places decimal.   0.63 / 9= 0.7   Answer is 0.7.
Answer: E
In a dairy farm, 20 cows eat 10 bags of husk in 40 days. In how many days one cow will eat one bag of husk?	Select the correct option:	A) 20	B) 40	C) 80	D) 30	E) 60

Solution: One cow eats 10/20= 
10/20 = 1/2 = around 0.5
0.5 bags of husk in 40 days. Then, it eats 1 bag in   40/0.5= 
  40/0.5 = 80
80 days   Answer: 80
Answer: C
At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using nine colors?	Select the correct option:
A) 21
B) 35
C) 84
D) 135
E) 210

Solution: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.   As an example, a chemical with the colors A/B/84 means that the following combinations 84ANNOT be used by any other chemical:   AB84   A84B   BA84   B84A   84AB   84BA   By extension, the first part of your calculation would be the number of possible substances that could be identified with 9 colors: 9c3 = 84 possible substances   84
Answer: C
HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are
Pick one
A) 30 and 75 B) 35 and 70 C) 40 and 65 D) 45 and 60 E) 55 and 70

Solution: Explanation:   Let the numbers be 15a and 15b. Then,   15a + 15b = 105 or a+ b = 7 .. (i)   LCM = 15ab = 180   ab = 12..(ii)   Solving equations (i) and (ii), we get a=4, b=3   So, the numbers are 15 ×4 and 15 ×3, i.e., 60 and 45   Answer: 45 and 60
Answer: D
Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $60.00 on four CDs and five tapes, how much does one tape cost?
Choose the most appropriate option
A) $5.00
B) $6.00
C) $12.00
D) $25.00
E) $100.00

Solution: CD => C   Type => T   Carol: 4C+5T=60   Anna: 12C+5T=120   12C-4C=60   8C=60   C=7.5   4C+5T=60   30+5T=60   5T=30   T=6   Answer is $6.00
Answer: B
A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 12 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
Choose one:	A) 2000	B) 1900	C) 1800	D) 1884	E) 1600

Solution: Pretty simple actually   Number of 1 letter symbols = 12   Number of 2 letter symbols = 12*12   Number of 3 letter symbols = 12*12*12   The answer is sum of the 3. = 12 +12*12 + 12*12*12 = 12*(1+12+144) =12*157= 
12*157 = 1_884
1884   So the answer is 1884.
Answer: D
A number exceeds by 25 from its 3/8 part. Then the number is?	Select.
A) 40	B) 25	C) 20	D) 30	E) 35

Solution: x â€“ 3/8 x = 25   x = 40   40NSWER 40
Answer: A
one out of five employees are capable of doing a certain task. 50 percent of the five employees, including the one who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?  Options:  A) 43.33%  B) 33.33%  C) 50%  D) 38.33%  E) 23.33%

Solution: Given 40% of 5 employees including 1 who are capable of doing task.   40% of 5 employeees   = 40/100 * 5= 
40/100 * 5 = 2
2 employees===> 1 employees who are capable of doing the task and one employee who is not capable.   percentage of employees assigned who are not capable   = 1/2 * 100= 
1/2 * 100 = 50
50%   ANSWER:50%
Answer: C
A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 4000 a year. What is his average monthly income? Options.
A) 2000  B) 2010  C) 2100  D) 2200  E) 2300

Solution: Total expenditure for the first 3 months = 3 × 1600 = 4800   Total expenditure for 4 months = 4 × 1550 = 6200   Total expenditure for 5 months = 5 × 1800 = 9000   Total expenditure and saving (which is income for one year)   = 4800 + 6200 + 9000 + 4000 = Rs. 24000   So, Average monthly income = 24000/12 = Rs. 2000   2000
Answer: A
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:10 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other? Choose the correct choice from the following answers
A) 0.5 + (p - 0.5s)/(r + s)	B) (p - 0.5s)/(r + s)	C) 0.5 + (p - 0.5r)/r	D) (p - 0.5r)/(r + s)	E) 0.5 + (p - 0.5r)/(r + s)

Solution: The distance 0.5 + (p - 0.5s)/(r + s) is going to cover between 1:00 and 1:30   = .5r   now the distance between the two trains = (p-.5r)   the relative velocity = (r-(-s)) = r+s   From 1:30, time is going to take when they meet = (p-.5r)/(r+s)   so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]   ans is 0.5 + (p - 0.5s)/(r + s)
Answer: A
The average age of 17 students of a class is 17 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 17th student is
Select the correct option
A) 62
B) 66
C) 18
D) 75
E) 12

Solution: Explanation:   Age of the 17th student = [17 * 17 - (14 * 5 + 16 * 9)] = (289-214)= 
(289-214) = 75
75 years.   Answer: 75
Answer: D
If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average Y (arithmetic mean) annual increase in the index over this period?  Choose the correct answer.
A) (x + 100)/18  B) x/18  C) (100 − x)/18  D) (x − 100)/18  E) 100x/18

Solution: CPI in end of 1967 = 100   CPI in end of 1985 = x   Number of years = 18   Average annual increase in CPI Y= (x-100)/18   Answer (x − 100)/18
Answer: D
If 1,000 microns = 1 decimeter, and 1,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?  Select the correct option: A) 100 B) 10 C) 1,000 D) 10,000 E) 100,000

Solution: Given that 1,000 microns = 1 decimeter =1,000,000 angstroms   So, 1 micron = 1,000,000/1,000   =1,000   Answer : 1,000
Answer: C
Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability M that Kate has more than $10 but less than $15? Select the correct option
A) 5/16 B) 1/2 C) M=12/30 D) M=15/32 E) M=3/8

Solution: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities are 3 or 4 heads.   I made an educated guess and it worked fine.   Ans- 'D'   MGMAT's anagram helped here as well.   HHHHT = 5!/4!*1! = 5   HHHTT = 5!/3!*2! = 10   Total acceptable cases = 15   Total cases = 32   P = 15/32.M=15/32
Answer: D