MU-NLPC/Calc-aqua_rat huggingface dataset:
The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average? Choose one:	A) 72	B) 77	C) 26	D) 27	E) 29

Solution: Sum of the marks for the 12 students   = 12 * 36= 
12 * 36 = 432
432. The marks of each student are doubled, the sum also will be doubled.   The new sum= 432 * 2= 
432 * 2 = 864
864. So, the new average= 864/12= 
864/12 = 72
72.   72nswer:72
Answer: A
How many ways are there to split a group of 8 boys into two groups of 4 boys each? (The order of the groups does not matter) Options.
A) 24 B) 35 C) 43 D) 60 E) 72

Solution: 8C4 = 70   If we consider these groups, each group will be counted twice.   The number of ways to choose 2 groups of 4 is  70/2= 
 70/2 = 35
35   The answer is 35.
Answer: B
A man swims downstream 65 km and upstream 35 km taking 5 hours each time; what is the speed of the current?
Select
A) 2
B) 3
C) 5
D) 7
E) 9

Solution: 65 --- 5 DS = 13   ? ---- 1   35 ---- 5 US = 7   ? ---- 1 S = ?   S = (13 - 7)/2= 
(13 - 7)/2 = 3
3   Answer: 3
Answer: B
x, a, z, and b are single digit positive integers. x = 1/8 a. z = 1/8 b. (10a + b) – (10x + z) could NOT equal	Choose the correct option:  A) 28  B) 35  C) 49  D) 63  E) 55

Solution: a=8x , b =8z therefore(8x.10+8z) - (10x +z) = (8-1) (10x+z) =7.(10x+Z)   number should be divisible by 7   55
Answer: E
A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?	Choose the correct choice from the following choices.
A) 3 1/5 Km B) 3 2/5 Km C) 3 3/5 Km D) 4 1/5 Km E) 5 1/5 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km)
Answer: A
The average of fifteen results is 593 and that of the first fourteen is 594. The fifteenth result is?  Choose the correct choice
A) 575	B) 602	C) 579	D) 586	E) 592

Solution: 15 * 593 â€“ 14 * 594 = 579   Answer: 579
Answer: C
Sequence A consists of 16 consecutive integers. If -6 is the least integer in sequence A, what is the range of the positive integers in sequence A?
Choose one.
A) 16
B) 15
C) 9
D) 8
E) 7

Solution: Since set A consists of 16 consecutive integers and -6 is the least integer then set A is consecutive integers from -6 to 9, inclusive: 9-(-6)+1= 
9-(-6)+1 = 16
16.   The range of positive integers in sequence A is 9-1= 
9-1 = 8
8.   Answer: 8.
Answer: D
The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?	Pick one
A) (3+x)(2−x) ≤ 0  B) (3−x)(2+x) ≥ 0  C) (x−3)(x+2) ≤ 0  D) (x+3)(2−x) ≥ 0  E) (3−x)(2−x) ≥ 0

Solution: Given: x≥−3x≥−3 and x≤2 x≤2   (x+3)≥0(x+3)≥0 and (x−2)≤0(x−2)≤0   (x+3)≥0(x+3)≥0 and (2−x)≥0(2−x)≥0   Answer: (x+3)(2−x) ≥ 0
Answer: D
If n is an integer and n^4 is divisible by 9, which of the following could be the remainder when n is divided by 9?  Pick one:  A) 1  B) 3  C) 5  D) 6  E) 8

Solution: option 1   Remainder 1 means  9+1= 
 9+1 = 10
10   n^4= 10^4= 10*10*10*10/9 is not an integer   option 2   Remainder 3 means  9+3= 
 9+3 = 12
12   n^4= 12*12*12*12/9 is an integer means n^4 is divisible by 9 if we take n=3   so 3 is correct
Answer: B
An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
Select the correct option:
A) 0.2974
B) 0.6976
C) 0.7565
D) 1.6465
E) 2.3475

Solution: Required probability:   =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)   =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002   =0.6976=0.6976   Edit: Thank you Vaibhav for providing an alternative method.   Alternate Method:   probability that the plane is hit when all the four shots are fired,   P=1−probability of not hitting the targetP=1−probability of not hitting the target   =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)   =1−0.3024=1−0.3024   =0.6976   0.6976
Answer: B
A boat can travel with aspeed of 20km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 125km downstream.  Pick: A) 1 hr B) 2 hrs C) 3 hrs D) 4 hrs E) 5 hrs

Solution: Speed downstream = (20 + 5) km/hr = 25 km/hr.   Time taken to travel 125 km downstream = 125/25= 
125/25 = 5
5 hrs.   Answer : 5 hrs
Answer: E
Dacid obtained 73, 69, 92, 64 and 82 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Choose one:
A) 79	B) 99	C) 88	D) 88	E) 76

Solution: Average = (73+ 69+ 92+ 64+82)/5   = 380/5= 
380/5 = 76
76   Answer:76
Answer: E
What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
Choose the most appropriate option
A) Rs.9688 B) Rs.9687 C) Rs.3338 D) Rs.9632 E) Rs.9680

Solution: Rs.9680xplanation:   A= P{1 + R/100}n   => 8000{1 + 10/100}2 = Rs.9680   Answer: Rs.9680
Answer: E
Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.  Choices
A) 228	B) 266	C) 289	D) 300	E) 271

Solution: Let the distance travelled be x km.   Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11 => x = 300 km.Answer: 300
Answer: D
Sides of a rectangular park are in the ratio 3: 2 and its area is 7350 sq m, the cost of fencing it at 50 ps per meter is?  Choose the correct choice from the following answers:
A) 287	B) 1287	C) 125	D) 988	E) 175

Solution: 3x * 2x = 7350 => x = 35   2(105 + 70) = 350 m   350 * 1/2 = Rs.175   Answer: 175
Answer: E
Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Pick one:
A) 7.18	B) 7.12	C) 7.1	D) 7.15	E) 7.11

Solution: T = (121 + 165)/ (80 + 65) * 18/5   T = 7.15   Answer:7.15
Answer: D
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 2:3. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture? Choose the correct answer.
A) 2:5
B) 3:5
C) 2:3
D) 3:2
E) 5:3

Solution: ............................... Water ............... Milk ....................... Total   Initial ...................... 24 .................... 16 .............................. 40   20 Lts mix. taken out 24-12 ............... 16-8 ........................... 40-20   20 Lts milk added..... 12+20 ................ 8 .............................. 40   20 Lts mix. taken out 32-16 ............... 8-4 ........................... 40-20   20 Lts water added..... 16 ................ 4+20 .............................. 40   New ratio = 24:16 = 3:2   3:2
Answer: D
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 13260, how much money did he borrow?	Choose the correct choice from the following choices.
A) 13000  B) 80288  C) 2668  D) 2600  E) 2781

Solution: Let the sum be Rs. x. Then,   [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 13260   18x + 45x + 39x = (13260* 100)   102x = 1326000 => x = 13000.   13000nswer:13000
Answer: A
The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/5. What is the probability of Michael passing his driving test?  Choose one
A) 1/24.  B) 4/5.  C) 1/3.  D) 2/3.  E) 2/5

Solution: 1/4 *1/m= 1/5 , 1/m = 4/5   Answer 4/5.
Answer: B
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?	Choose the correct choice from the following choices:
A) 70%
B) 20%
C) 90%
D) 27%
E) 22%

Solution: 900 ---- 180   100 ---- ? => 20%   Answer: 20%
Answer: B
What is the value of (P + Q)/(P - Q) if P/Q is 8? Answers:
A) 4/3 B) 2/3 C) 2/6 D) 7/8 E) 9/7

Solution: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]   = (8 + 1)/(8 - 1)   = 9/7   ANSW9/7R:9/7
Answer: E
On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
Select
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Number=56x+29 (∵ since the number gives 29 as remainder on dividing by 56)   =(7×8×x)+(3×8)+5   Hence, if the number is divided by 8, we will get 5 as remainder.   ANSWER:5
Answer: D
When asked what the time is,a person answered that the amount of time left is 1/5 of the time already completed.what is the time.  Choose the correct choice:  A) 2  B) 9  C) 3  D) 8  E) 6

Solution: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)   24−x=15x⇒x=2024−x=15x⇒x=20   Time is 8 PM   Answer:8
Answer: D
The price of commodity X increases by 45 cents every year, while the price of commodity Y increases by 20 cents every year. In 2001, the price of commodity X was $5.20 and the price of commodity Y was $7.30. In which year will the price of commodity X be 35 cents less than the price of commodity Y?
Choose the correct answer:
A) 2006
B) 2007
C) 2008
D) 2009
E) 2010

Solution: The price of commodity X increases 25 cents each year relative to commodity Y.   The price difference is $2.10 and commodity X needs to be 35 cents less than commodity Y.   $1.75 / 25 cents = 7 years   The answer is   2001 + 7= 
  2001 + 7 = 2_008
2008.   The answer is 2008.
Answer: C
What was the day of the week on 11th March, 2006?
Choose the correct answer
A) Monday	B) Friday	C) Thursday	D) Sunday	E) Saturday

Solution: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)   Odd days in 1600 years = 0   Odd days in 400 years = 0   5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days   Jan. Feb. March   (31 + 28 + 11 )= 
(31 + 28 + 11 ) = 70
70 days   70 days= (6 weeks + 0 day) 1 odd day.   Total number of odd days = (0 + 0 + 6 + 0)= 
(0 + 0 + 6 + 0) = 6
6 0 odd day.   Given day is Saturday.   Answer: Option Saturday
Answer: E
Find the ratio in which wheat of inferior quality (Rs.14/kg) be mixed with wheat of superior quality (Rs.28/kg) so that the shopkeeper gains Rs.2 by selling the resulting mixture at Rs.20/kg.
Choose the correct choice from the following.
A) 1 : 3 B) 5 : 2 C) 3 : 4 D) 2 : 5 E) None of these

Solution: Explanation:   Let the resulting mixture be 1 kg, and x kg be the amount of wheat of inferior quality.   Therefore, (1-x)kg is the amount of wheat of superior quality.   As the shopkeeper gains Rs.2, the cost of the mixture is Rs.18   14*x + 28*(1-x) = 18   14x - 28x + 28 = 18   14x = 10   x = 5/7   (1 – x) = 2/7   x : (1-x) = 5/7 : 2/7   = 5 : 2   ANSWER 5 : 2
Answer: B
In a fuel station the service costs $2.05 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 140% bigger and they are all empty-?  Choose the most appropriate option
A) 122.6$  B) 128.9$  C) 243.7$  D) 298.85$  E) 314.45$

Solution: Service cost of 3 van and 2 truck = 2.05*(3+2)=10.5   Fuel in 3 Van = 3*65= 
3*65 = 195
195 litre   Fuel in 2 Trucks=2 * 65(1+140/100)= 312   Total fuel(Van+Truck) = 507 Litre   Total Fuel cost = 507*0.6= 
507*0.6 = 304.2
304.2   TOTAL COST=FU314.45$L+S314.45$RVIC314.45$=304.2+10.25= 
304.2+10.25 = 314.45
314.45   ANSW314.45$R IS 314.45$
Answer: E
20% of A is B, then B% of 20 is same as what?	Choices:
A) 7% of A	B) 4% of A	C) 8% of A	D) 1% of A	E) 3% of A

Solution: Explanation:   It is given that 4% of A measures 20% of A   => So, 20% of A = 4% of A or 20/100 * A = 4% of A - (1)   4% of A% of 20= 4% of A/100 X 20= 24% of A/10 ---(2)   => Now, 4% of A% of 20   Substituting (1) in (2) we get   2*(2A/10) / 10= 4A/100   Hence, 4% of A% of 20 = 4% of A   ANSWER: 4% of A
Answer: B
A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum N of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?	Choose the correct answer
A) 5 B) 7 C) 9 D) 10 E) 14

Solution: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum N of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is 10, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.10
Answer: D
30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?  Pick one:
A) 60%
B) 70%
C) 80%
D) 90%
E) 100%

Solution: Explanation :   Let total number of men = 100   Then   80 men are less than or equal to 50 years old   (Since 80% of the men are less than or equal to 50 years old)   => 20 men are above 50 years old (Since we assumed total number of men as 100)   20% of the men above the age of 50 play football   ⇒Number of men above the age of 50 who play football = 20× (20/100) = 4   Number of men who play football = 20 (Since 20% of all men play football)   Percentage of men who play football above the age of 50 = (4/20) × 100=20%   =>Percentage of men who play football less than or equal to the age 50 = 100%−20%=80%   ANSWER IS 80%
Answer: C
A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than seven people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month? Choose the correct option.
A) 2x/35
B) 4x/15
C) x/7
D) 3x/20
E) 5x/7

Solution: If 7 people share the rent, each person would pay x/7.   If 5 people share the rent, each person will pay x/5.   The extra amount each person pays is x/5 - x/7 = 7x/35 - 5x/35 = 2x/35   The answer is 2x/35.
Answer: A
Missing number in the series
4 9 20 43 90 185 376 759 1526 ?	Choose the correct answer:  A) 3750  B) 3061  C) 3903  D) 3952  E) 3804

Solution: 4*2+1= 
4*2+1 = 9
9   9*2+2= 
9*2+2 = 20
20   20*2+3= 
20*2+3 = 43
43   43*2+4= 
43*2+4 = 90
90   90*2+5= 
90*2+5 = 185
185   185*2+6= 
185*2+6 = 376
376   376*2+7= 
376*2+7 = 759
759   759*2+8= 
759*2+8 = 1_526
1526   1526*2+9= 
1526*2+9 = 3_061
3061   ANSWER:3061
Answer: B
Average of five numbers is 12. If one number is excluded the average becomes 10. The excluded number is  Pick
A) 35	B) 20	C) 40	D) 30	E) 67

Solution: Explanation:   Number is (5*12) - (4*10) = 60-40= 
60-40 = 20
20   Answer: Option 20
Answer: B
20 men do a work in 20days. How many men are needed to finish the work in 5days?
Choose the correct choice from the following:
A) 50	B) 20	C) 80	D) 10	E) 15

Solution: men required to finish the work in 5days = 20*20/5= 
20*20/5 = 80
80   Answer is 80
Answer: C
In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 70π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
Options:
A) 1000π	B) 400π	C) 280π	D) 200π	E) 20π

Solution: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.   4(70π) = 280π   The answer is 280π.
Answer: C
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?	Choose the correct choice from the following answers
A) 3999  B) 3000  C) 3882  D) 2661  E) 1234

Solution: 60*5:36*6:75*3   100: 72: 75   100/247 * 7410= 
100/247 * 7410 = 3_000
3000   Answer: 3000
Answer: B
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 12% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?	Pick.
A) 5%  B) 10%  C) 15%  D) 21%  E) 31%

Solution: 60-(x+12+z) + 50-(x+12+y) + 35-(z+12+y) + x + y + z +12 = 100   where x = people who bought MilkChicken   y = people who bought chickenApples   z= people who bought Milk and Apples   x+y+z= the number of people who bought just exactly two products.   Hence solving the above equation we get,   121 -(x+y+z) = 100   Thus, x+y+z= 21   Answer: 21%
Answer: D
Can you find the last number in the number sequence given below?
10 : 10 : 20 : 45 : 110 : 300 : ?
Pick one
A) 930	B) 870	C) 450	D) 330	E) 220

Solution: 930   New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)   10   10 * 0.5 + 5= 
10 * 0.5 + 5 = 10
> 10   10 * 1.0 + 10= 
10 * 1.0 + 10 = 20
> 20   20 * 1.5 + 15= 
20 * 1.5 + 15 = 45
> 45   45 * 2.0 + 20= 
45 * 2.0 + 20 = 110
> 110   110 * 2.5 + 25= 
110 * 2.5 + 25 = 300
> 300   300 * 3.0 + 30= 
300 * 3.0 + 30 = 930
> 930 , desired answer
Answer: A
How many seconds will a 450 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Pick:  A) 20  B) 27  C) 42  D) 32  E) 60

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 450 * 3/50= 
450 * 3/50 = 27
27 sec.   Answer: Option 27
Answer: B
A boy has three trousers and 8 shirts. In how many different ways can he select a trouser and a shirt?
Answers:
A) 24 ways B) 27 ways C) 28 ways D) 18 ways E) 19 ways

Solution: The boy can select one trouser in three ways.   The boy can select one shirt in 8 ways.   The number of ways in which he can select one trouser and one shirt is   3 * 8= 
  3 * 8 = 24
24 ways.   24 waysnswer:24 ways
Answer: A
How many number from 11 to 50 are there which are exactly divisible by 7 but not by 3?
Pick one
A) 2
B) 4
C) 5
D) 6
E) 7

Solution: 14,28,35,49   ANSWER:4
Answer: B
Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 38 square meters. What is the area that is covered with three layers of wallpaper?	Choose the correct choice from the following answers.
A) 5 Square Meters  B) 36 Square Meters  C) 42 Square Meters  D) 83.3 Square Meters  E) 41 Square Meters

Solution: 300 - 180= 
300 - 180 = 120
120 sq m of the wallpaper overlaps (in either two layers or three layers)   If 36 sq m has two layers, 120 - 38= 82 sq m of the wallpaper overlaps in three layers. 82 sq m makes two extra layers hence the area over which it makes two extra layers is 41 sq m.   Answer (41 Square Meters).
Answer: E
Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?	Choose one.
A) 7 hrs 30 min
B) 8 hrs
C) 8 hrs 15 min
D) 8 hrs 25 min
E) 9 hrs

Solution: Explanation:   Number of pages typed by Ronald in 1 hour = 32/6 = 16/3   Number of pages typed by Elan in 1 hour = 40/5= 
40/5 = 8
8   Number of pages typed by both in 1 hour= (16/3 + 8) = 40/3   Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min   ANSWER IS 8 hrs 15 min
Answer: C
If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
I.	28
II.	36
III.	42 Choices.
A) I only	B) II only	C) I and II only	D) I and III only	E) I, II, and III

Solution: x+y=30 & y+z=20 so x+2y+z=50   x+y+z=50-y   If perimeter is 28 then y=50-28= 
50-28 = 22
22, and y+z=20 z cannot be negative. I is out.   If perimeter is 36 then y=50-36= 
50-36 = 14
14. z=6, x=16. no problem here.   If perimeter is 42 then y=50-42= 
50-42 = 8
8. x=22, z=12. x cannot be greater than sum of y & z. III is out.   II only is answer.
Answer: B
n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 27 ?  Choose the correct choice.
A) 0.1  B) 0.2  C) 0.25  D) 0.3  E) 0.05

Solution: Set N: there is 4 ways to chose a number   Set P: there is 5 ways to chose a number   so total outcome is  4*5= 
 4*5 = 20
20 which is represent 20 pairs of number   now we have 1 pairs can give us 27 which are (9,18)   1/20= 
1/20 = 1/20 = around 0.05
0.05   Answer 0.05
Answer: E
A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes jerry can make using this recipe? Answers.
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.   Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.   Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.   answer is 5
Answer: A
If x/4 years ago Roger was 21 years old and x/4 years from now he will be 4x years old, how old will he be 5x years from now?  Choose the correct choice from the following options:
A) 32	B) 35	C) 30	D) 40	E) 70

Solution: Assume the current age = a   a - x/4 = 28 (i)   a + x/4 = 4x   Or a = 15x/4 (ii)   Putting the value of a from (ii) in (i)   15x/4 - x/4 = 28   Or 14x/4 = 28 Therefore x = 8 and a = 30   5x years from now, age will be  30 + 5*8= 
 30 + 5*8 = 70
70   Option 70
Answer: E