mathewhe/aqua_rat huggingface dataset:
Question: There are 20 brown dogs, 10 white dogs, 15 black dogs.Totally how many dogs are there in all?
(A) 45
(B) 15
(C) 25
(D) 5
(E) 30
Rationale: 20+10+15=45. Answer is A
Answer: (A) 45
Question: The Guests at a football banquet consumed a total of 327 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
(A) 160
(B) 161
(C) 162
(D) 163
(E) 164
Rationale: To minimize one quantity maximize other.
163*2 (max possible amount of food a guest could consume) = 326 pounds, so there must be more than 163 guests, next integer is 164.
Answer: E.
Answer: (E) 164
Question: A goods train runs at the speed of 72 km/hr and crosses a 270 m long platform in 26 sec. What is the length of the goods train?
(A) 278
(B) 166
(C) 151
(D) 250
(E) 109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 270)/26 = 20
x = 250 m.
Answer:D
Answer: (D) 250
Question: A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
(A) 45
(B) 50
(C) 55
(D) 65
(E) none
Rationale: Sol.
A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.
∴ C’s rent = Rs. [175 * 9/35] = Rs. 45.
Answer A
Answer: (A) 45
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
(A) 720 ways
(B) 735 ways
(C) 767 ways
(D) 723 ways
(E) 730 ways
Rationale: The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer:A
Answer: (A) 720 ways
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.13 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 1276
(B) 1560
(C) 2832
(D) 1299
(E) 1236
Rationale: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 13 = 1560
Answer: Option B
Answer: (B) 1560
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.460 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
(A) 450
(B) 470
(C) 560
(D) 700
(E) 510
Rationale: Let no. of non- officers be x
15 * 460 + x * 110 = (x + 15) 120
x = 510
E
Answer: (E) 510
Question: Difference between the length &breadth of a rectangle is 10 m. If its perimeter is 60 m, then its area is??
(A) 2000 m^2
(B) 200 m^2
(C) 2520 m^2
(D) 2556 m^2
(E) 2534 m^2
Rationale: l -b = 10
2 (l+b)= 60 => l + b = 30
2 l = 40 => l = 20 so b = 10
area of the rectangle = l x b = 20 x 10 = 200 m^2
Answer : B
Answer: (B) 200 m^2
Question: The bankerâ€™s gain on a sum due 3 years hence at 10% per annum is Rs. 60. The bankerâ€™s discount is
(A) Rs.960
(B) Rs.840
(C) Rs.1020
(D) Rs.760
(E) Rs.260
Rationale: Solution
T.D	=(B.G x 100 / R x T)
= Rs.(60x100/10 x 3)
= Rs.200.
B.D
=Rs(200+ 60)
= Rs.260.
Answer E
Answer: (E) Rs.260
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(A) 124
(B) 129
(C) 132
(D) 142
(E) 144
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: If a,b are positive integers and a/b=77.75 which of the following could be the value of b?
(A) 1. 25
(B) 2. 26
(C) 3. 27
(D) 4. 27
(E) 4. 32
Rationale: Given a/b = 77.75.
this is 77 and 3/4 = 311/4
Since a and b are integers we know that whatever is the value of b, it must be divisible by 4 completely(to make a an integer)
Ans:E
Answer: (E) 4. 32
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
(A) $5500
(B) $11000
(C) $22000
(D) $2750
(E) $44000
Rationale: Explanatory Answer
Shawn received an extra amount of ($605 - $550) $55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.
The extra interest earned on the compound interest bond = $ 55
The interest for the first year = $550/2 = $ 275
Therefore, the rate of interest = (55/275)*100 = 20% p.a.
20% interest means that Shawn received 20% of the amount he invested in the bonds as interest
If 20% of his investment in one of the bonds = $275, then his total investment in each of the bonds = (275/20)*100 = $ 1375
As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = $ 2750.
correct choice is (D)
Answer: (D) $2750
Question: How is 4% expressed as a decimal fraction?
(A) 0.4
(B) 0.04
(C) 0.004
(D) 0.0004
(E) 4
Rationale: 4/100= 0.04
ANSWER:B
Answer: (B) 0.04
Question: Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game. How many teams participated in the race?
(A) 32
(B) 77
(C) 279
(D) 27
(E) 91
Rationale: Total five rounds were run. So in the final round 2 teams must have participated. In the penultimate round 4 teams, and 3rd round 8, 2nd round 16 and in the first round 32 teams must have participated as in each round half of the teams got eliminated.
Answer:A
Answer: (A) 32
Question: Two trains A and B are 175 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
(A) 10 s
(B) 6 s
(C) 4 s
(D) 8 s
(E) 13 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 175 + 150 = 325 m. Time taken =325/25 = 13 s.
CORRECT ANSWER E.
Answer: (E) 13 s
Question: In how many ways can a committee of 4 people comprising at least 3 boys be formed using a group of 4 boys and 6 girls?
(A) 67
(B) 64
(C) 65
(D) 66
(E) None of these
Rationale: There are 2 options: the selected groups have no girls or one girls.
-First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10 = 60
-Second case: 4 boys: 5C4 = 5
So there are 60 + 5 = 64 ways in total.
B
Answer: (B) 64
Question: A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $204, what is the fewest number of $3 Frisbees that could have been sold?
(A) 24
(B) 12
(C) 8
(D) 52
(E) 2
Rationale: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.
To solve, we have 2 equations and 2 unknowns
Let x = number of $3 Frisbees sold
Let y = number of $4 Frisbees sold
x + y = 64
3x + 4y = 204
x = 64 - y
3(64-y) + 4y = 204
192 - 3y + 4y = 204
y = 12 x= 64-12= 52
D
Answer: (D) 52
Question: water is continuously poured from a reservoir to a locality at the steady rate of 10,000 liters per hour. When delivery exceeds demand the excess water is stored in a tank. If the demand for 8 consecutive three-hour periods is 10000,10000,45000,25000,40000,15000,60000 and 35000 liters respectively, what will be the minimum capacity required of the water tank (in 1000 litres) to meet the demand?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: in the period of first 3 hrs, the demand of water = 10000.
but the water poured by 10000 per hour.
Thus the end of 3 hours it will poured 30000 ltr then the excess of water = 20000.
Similarly at the end of 2nd 3 hr period the excess of water 20000+20000 = 40000.
Third, 3 hrs water poured = 30000
already we have 40000 of excess water and demand 45000.
Then the excess water at the end of 3rd 3 hrs
= 40000+30000–45000
= 25000
Fourth 3 hrs. water = 25000+30000–25000
= 30000
Fifth = 30000+30000–40000
= 20000
Sixth = 20000+30000–15000=35000
Seventh = 35000+30000–60000
= 5000
Eighth = 5000+30000–35000
= 0
By analyzing the above results, we have 40000 ltrs is the highest measure of excess water.
So the minimum capacity of water tank = 40000 litres = 40
i.e. = 40
ANSWER:C
Answer: (C) 40
Question: If an article is sold at 18% profit instead of 11% profit, then the profit would be $56 more. What is the cost price?
(A) $600
(B) $800
(C) $1000
(D) $1200
(E) $1400
Rationale: 7% * cost price = $56
1% * cost price = $56 / 7 = $8
The cost price is $800.
The answer is B.
Answer: (B) $800
Question: If the tens digit of positive integers x, y are 6, how many values of the tens digit of 2(x+y) can be there?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If X=y=60, 2(x+y)=240 is derived. If x=y=69, 2(x+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
Answer: (C) 4
Question: Three-fourth of a positive number and 25/216 of its reciprocal are equal. The number is:
(A) 5/12.72
(B) 12/5
(C) 25/144
(D) 144/25
(E) 146/25
Rationale: Let the number be x. Then,
3/4 x = 25/216 * 1/x
x2 = 25/216 * 4/3 = 25/162
x = 5/12.72
ANSWER:A
Answer: (A) 5/12.72
Question: The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 6 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: 6C1*6C2 = 6*15 = 90
The answer is D.
Answer: (D) 90
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) Rs.4589
(B) Rs.4528
(C) Rs.4528
(D) Rs.4530
(E) Rs.4537
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs.4530
Answer:D
Answer: (D) Rs.4530
Question: In N is a positive integer less than 200, and 27N/60 is an integer, then N has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: (A).
27n/60 must be an integer. => 9n/20 must be an integer. Hence n must be a multiple of 2*5.
=> n has 2 different prime integers.
Answer: (A) 2
Question: Adding 20% of x to x is equivalent to multiplying x by which of the following?
(A) 12.5
(B) 1.05
(C) 1.15
(D) 1.2
(E) 1.25
Rationale: 120x/100= 1.2*x
ANSWER:D
Answer: (D) 1.2
Question: Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations T of classes are available?
(A) 3
(B) T=6
(C) T=7
(D) T=9
(E) T=12
Rationale: I think it should be E only.
No where it is given that he attends different classes on each day.
Experts please provide your views.
--- EDITED my Response. It was a typo. I meant 12 is the answer.
If only Day 1 : 3 options
If Day 1 and Day 2 : 3*3 = 9 Options
So, Total = 3+9= 12.
Answer: (D) T=9
Question: How many different possible arrangements A can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
(A) 360
(B) 720
(C) 900
(D) 1800
(E) 5040
Rationale: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans A= 7!/ (2!2!) -6!/2! = 900
HENCE C.
Answer: (C) 900
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) 278
(B) 270
(C) 876
(D) 279
(E) 367
Rationale: I = (500*9*6)/100
= 270
Answer: B
Answer: (B) 270
Question: . Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2000
(B) 2009
(C) 2007
(D) 20054
(E) 2002
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: (A) 2000
Question: At 6′o a clock ticks 6 times. The time between first and last ticks is 20 seconds. How long does it tick at 12′o clock
(A) 47
(B) 76
(C) 44
(D) 66
(E) 11
Rationale: Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 20/5 = 4 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 4 = 44 secs.
Answer: C
Answer: (C) 44
Question: How much 50% of 56 is greater than 30% of 50?
(A) 18
(B) 99
(C) 13
(D) 55
(E) 71
Rationale: (50/100) * 56 – (30/100) * 50
28 - 15 = 13
Answer: C
Answer: (C) 13
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
(A) 10
(B) 15
(C) 12
(D) 16
(E) 18
Rationale: Explanation:
1/6 â€“ 1/15 = 1/10 => 10
ANSWER IS A
Answer: (A) 10
Question: The closest approximation of F(69.28 × 0.004)/0.03 is
(A) 0.092
(B) 0.92
(C) 9.2
(D) 92
(E) 920
Rationale: F(69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.C
Answer: (C) 9.2
Question: The number of natural numbers n such that (n+1)^2/(n+7) is an integer, is ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: we can use (n+1)^2 greater than (n+7) which gives n>2,-3........now there are four integers -2.-1,0,1 in between -3 and 2.
so answer is 4.
ANSWER:A
Answer: (A) 4
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?
(A) 5, 12, and 8 kg
(B) 6, 12, and 8 kg
(C) 7, 12, and 8 kg
(D) 8, 12, and 8 kg
(E) None
Rationale: Solution:
Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2x+2, respectively. So
x+2x+x+2=26
4x=24
x=6
Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.
Answer B
Answer: (B) 6, 12, and 8 kg
Question: If a = 105 and a^3= 21 * 25 * 315 * b, what is the value of b?
(A) 35
(B) 7
(C) 45
(D) 49
(E) 54
Rationale: First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
25 = 5 * 5
315 = 3 * 3 * 5*7
so, (105)^3 = 3 * 7 * 5 * 5 * 3 *3 *5*7 *b
Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^3 * 7^2 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^3 * 7^2
b = 7
Correct answer B.
Answer: (B) 7
Question: A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price?
(A) Rs.540/-
(B) Rs.560/-
(C) Rs.580/-
(D) Rs.590/-
(E) Rs.600/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
Option 'A'
Answer: (A) Rs.540/-
Question: A single discount equivalent to the discount series of 15%, 10% and 5% is?
(A) 27.325
(B) 31.0
(C) 31.6
(D) 31.1
(E) 31.5
Rationale: 100*(85/100)*(90/100)*(95/100)
= 68.4
100 - 72.675 = 27.325
Answer: A
Answer: (A) 27.325
Question: If n is a prime number, which of the following could be true
(A) n^n=n
(B) n^2/4= is even
(C) (n)(n^n) = is negative
(D) n^n/4 = 1^(n-1)
(E) n^2+n^3= n^5
Rationale: D should be the answer.
2^2/4 = 1^(2-1)
Answer: (D) n^n/4 = 1^(n-1)
Question: What is the product of the greatest 2 digit multiple of 13 and the greatest 2 digit prime number?
(A) 9,312
(B) 9,408
(C) 9,506
(D) 8,827
(E) 9,702
Rationale: the greatest 2 digit multiple of 13: 91
the greatest 2 digit prime numebr: 97
97*91.
8827
D
Answer: (D) 8,827
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(3,3)
D=(1,4)
E=(8,0)
(A) 0.6
(B) 0.75
(C) 0.9
(D) 0.5
(E) 0.3
Rationale: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as D.
Answer: (D) 0.5
Question: H, Be, F, S, Mn, Kr, In, Gd, Tl, ?
What's the next in the sequence ?
(A) Fm
(B) Ks
(C) gh
(D) kl
(E) Zd
Rationale: A
Fm.
These are the chemical elements whose atomic numbers are perfect squares.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer: (A) Fm
Question: Pipe A can fill a tank in 12 hours. Due to a leak at the bottom, it takes 18 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 36
(B) 87
(C) 40
(D) 37
(E) 86
Rationale: Let the leak can empty the full tank in x hours 1/12 - 1/x = 1/18
=> 1/x = 1/12 - 1/18 = (3 - 2)/36 = 1/36
=> x = 36.
Answer: A
Answer: (A) 36
Question: A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 30
(D) 90
(E) 95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 160
16x = 160
x = 10.
Hence, total number of notes = 3x = 30.
Answer: Option C
Answer: (C) 30
Question: Two cars cover the same distance at the speed of 50 and 63 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 212 km
(B) 214 km
(C) 224 km
(D) 216 km
(E) 231 km
Rationale: 50(x + 1) = 63x
X = 3.85
60 * 3.85 = 231 km
ANSWER:E
Answer: (E) 231 km
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water in ?
(A) 10hr
(B) 14hr
(C) 12hr
(D) 9hr
(E) 15hr
Rationale: Work done by the leak in 1 hour = 1/2 - 3/7 = 1/14
Leak will empty the tank in 14 hrs
Answer is B
Answer: (B) 14hr
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
(A) 42
(B) 36
(C) 28
(D) 20
(E) 24
Rationale: Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/12 = 20 m/s
Speed of each train = v = 20/2 = 10 m/s
= 10×36/10 km/hr = 36 km/hr
Answer: Option B
Answer: (B) 36
Question: If 5a + 7b = l, where a and b are positive integers, what is the largest possible value of l for which exactly one pair of integers (a, b) makes the equation true?
(A) 35
(B) 48
(C) 69
(D) 70
(E) 74
Rationale: 5*a1 + 7*b1 = l
5*a2 + 7*b2 = l
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.
Lets check how it works for our numbers, starting from the largest:
E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad
D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus
D is the answer
Answer: (D) 70
Question: An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors does the number 4x have?
(A) 4y
(B) 3y
(C) 16y
(D) 5y
(E) Cannot be determined
Rationale: Let’s express x as a product of its prime factors:
x=2a∗3b∗5c∗…x=2a∗3b∗5c∗…
Total number of its positive divisors will be
(a+1)∗(b+1)∗(c+1)∗…=y(a+1)∗(b+1)∗(c+1)∗…=y
Now we’ll do the same for the 4x
4x=22∗2a∗3b∗5c∗…=2a+2∗3b∗5c…4x=22∗2a∗3b∗5c∗…=2a+2∗3b∗5c…
Total number of positive divisors of 4x will be
(a+3)∗(b+1)∗(c+1)…=y′(a+3)∗(b+1)∗(c+1)…=y′
For easier calculations let’s take (b+1)∗(c+1)∗…=z(b+1)∗(c+1)∗…=z
We have: (a+3)∗z=y′(a+3)∗z=y′
(a+1+2)∗z=y′(a+1+2)∗z=y′
(a+1)∗z+2∗z=y′(a+1)∗z+2∗z=y′
y+2∗z=y′y+2∗z=y′
So, as we can see, in order to find out the total # of positive divisors of 4x we need to know # of odd divisors of x, which is not given in the question.
Answer E.
Answer: (E) Cannot be determined
Question: What is Sonia’s present age?
I.	Sonia’s present age is five times Deepak’s present age.
II.	Five years ago her age was twenty-five times Deepak’s age at that time.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
I. S = 5D D = s/5….(i)
II. S – 5 = 25 (D – 5) <=> S = 25D – 120 ….(ii)
Using (i) in (ii), we get S =(25 x S/5) - 120
4S = 120.
S = 30.
Thus, I and II both together give the answer. answer is (E).
Answer: (E) Both I and II are necessary to answer
Question: 6 boys and 4 girls appeared in a exam. If 4 students are failed how many chances at least one girl is failed?
(A) 198
(B) 200
(C) 190
(D) 195
(E) 180
Rationale: 4 girls and 6 boys. Four students is failed
It is always better to subtract the total from none in case of at least one problems.
Total ways = 10C4 = 210
Total ways without any girls = 6C4 = 15
Hence ways in which at least one man will be present = 210 - 15 = 195
Correct option: D
Answer: (D) 195
Question: How long will a boy take to run round a square field of side 30 meters, if he runs at the rate of 12km/hr?
(A) 52sec
(B) 45sec
(C) 60sec
(D) 25sec
(E) 36sec
Rationale: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec
Distance = 30*4 = 120m
Time taken = 120*3/10 = 36sec
Answer is E
Answer: (E) 36sec
Question: A motor pool has 800 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
(A) 65%
(B) 52%
(C) 45%
(D) 30%
(E) 10%
Rationale: Trucks = 30% of 800 = 240
Other Vehicles (Excluding Trucks) = 800-240 = 560
Diesel Vehicle = 20% of 800 = 160 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 160-15 = 145
Trucks that are NOT diesel = 240 - 15 = 225
Other Vehicles that are NOT diesel Vehicles = 560-145 = 415
Required % = (415/800)*100 = 51.87%=52%
Answer: option B
Answer: (B) 52%
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $570 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
(A) 23,500
(B) 24,500
(C) 25,500
(D) 26,500
(E) 27,500
Rationale: Let the weekly sales of both = x
570+(x−1000)8/100=10/100x
x = 24500
ANSWER:B
Answer: (B) 24,500
Question: 46-3*4^2+15 = ?
(A) 287
(B) -13
(C) -73
(D) 13
(E) None
Rationale: 46-3*4^2+15
= 46-3*16+15=20-48+15=13..
D
Answer: (D) 13