divelab/Sys2Bench huggingface dataset:
Question: Sunitha’s age is 1/6th of her father’s age. Her father’s age will be twice of Varun’s age after 10 years. If Varun’s eight birthday was celebrated two years ago, then what is Sunitha’s present age?
Options:
A)30 years
B)24 years
C)6 years
D)7 years
E)None of these
Rationale: Varun’s present age = 8 + 2 = 10 yrs
F + 10 = 2 (V + 10) = 2 (10+ 10)
F = 30, S = 30/6 = 5 years.
Therefore its none of the these.
ANSWER:E
Answer: E
Question: Walking at 4/5 of her normal speed, a worker is 10 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: Let V be her normal speed and let T be her normal time.
D = (4/5)V * (T+10)
Since the distance is the same we can equate this to a regular day which is D = V*T
V*T = (4/5)V * (T+10)
T/5 = 8
T=40
The answer is C.
Answer: C
Question: What number comes next?
428, 693, 714, 286, 937, ?
Options:
A)142
B)231
C)245
D)148
E)123
Rationale: A
142
The numbers 42869371 are being repeated in the same sequence.
Answer: A
Question: A square, with perimeter 20, is inscribed in a circle. What is the area of the circle?
Options:
A)8π
B)11π
C)10π
D)12π
E)12.5π
Rationale: Area of circuscribed circle = pi/2*area of square
Area of square = (20/4)^2 = 5^2= 25
Area of circle = pi/2*4=12.5pi
Answer E
Answer: E
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/18%
B)18 2/11%
C)18 3/11%
D)18 2/17%
E)18 3/18%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: B
Question: A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 90 minutes later?
Options:
A)2(10^5)
B)9(10^5)
C)(2^9)(10^5)
D)(10^9)(10^5)
E)(10^5)^9
Rationale: Every 10 minutes, the population is double the previous population.
In 90 minutes, the population doubles 9 times.
The population then is 2^9*10^5.
The answer is C.
Answer: C
Question: If (a – b) is 17 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
Options:
A)6
B)2
C)3
D)7
E)5
Rationale: (a – b) – (c + d) = 17 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 17 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 17 and (b + d) = (c – a) – 3
=> (a – c) – 17 = (c – a) – 3 => 2(a – c) = 14 => (a – c) = 7
ANSWER:D
Answer: D
Question: In a game of 100 points,A can give B 20 points and C 28 points.Then, B can give C :
Options:
A)8 points
B)10 points
C)14 points
D)40 points
E)50 points
Rationale: Solution
A : B = 100 : 80 and A : C = 100 : 72.
∴ B/C=(B/C x A/C) = (80/100 x 100/72)= 10/9 =100/90= 100 : 90.
∴ B can give C 10 points.
Answer B
Answer: B
Question: The price for a loaf of bread in April was $1.17, in May the price was $1.32, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?
Options:
A)$1.16
B)$1.17
C)$1.18
D)$1.19
E)$1.20
Rationale: Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(117) + 132x + (4x/3)(108) / (2x/3 + x + 4x/3) =
(78 + 132 + 144) / (3) = 354/3 = $1.18
The answer is C.
Answer: C
Question: A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price B per t-shirt that the vendor paid for these purchases?
Options:
A)$12.20
B)$12.50
C)$12.55
D)$12.70
E)$13.00
Rationale: Correct Answer: A
Explanation: The relevant formula for this problem is Average B= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
Answer: A
Question: The average of 13 numbers is 60. Average of the first 7 of them is 54 and that of the last 7 is 61. Find the 8th number?
Options:
A)25
B)83
C)45
D)53
E)64
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 54 = 378
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 378 - 780 = 25.
Answer:A
Answer: A
Question: A shop that sells phone accessories had the following sales: 10 thousand earbuds at $10 each, 5300 phone cases at $12 each and 450 power banks at $50 each. What % of the shop's revenue is from power banks?
Options:
A)11.1%
B)12.1%
C)10.1%
D)9.1%
E)13.1%
Rationale: Correct Answer: B
The company's total revenue from earbuds=10000*$10=$100000
The company's total revenue from phone cases=5300*$12=$63600
The company's total revenue from power banks=450*$50=$22500
The combined total of all sales=$186100
Therefore % of power banks sales=22500/186100*100= 12.1%
Answer: B
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is
Options:
A)276
B)299
C)312
D)322
E)None
Rationale: Solution
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14)	= 322.
Answer D
Answer: D
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 25 minutes?
Options:
A)80
B)100
C)150
D)240
E)300
Rationale: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 25 minutes the population increases by 25 x 4 = 100 people.
Answer. B.
Answer: B
Question: The greatest number of 5 digits = 99999.
Options:
A)137
B)143
C)77
D)88
E)11
Rationale: Answer:B
Answer: B
Question: The Full House Casino is running a new promotion. Each person visiting the casino has the opportunity to play the Trip Aces game. In Trip Aces, a player is randomly dealt three cards, without replacement, from a deck of 8 cards. If a player receives 3 aces, they will receive a free trip to one of 10 vacation destinations. If the deck of 8 cards contains 3 aces, what is the probability that a player will win a trip?
Options:
A)1/336
B)1/120
C)1/56
D)1/720
E)1/1440
Rationale: P=P(ace in the first draw)*P(ace in the second draw)*P(ace in the third draw)=3/8*2/7*1/6=1/56.
Answer: C.
Answer: C
Question: A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train?
Options:
A)299
B)277
C)276
D)370
E)281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 150)/26 = 20
x = 370 m.
Answer: D
Answer: D
Question: If a certain number of people can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of people will require to dig earth 75m deep, 20m long and 50m broad.
Options:
A)12
B)18
C)6
D)1
E)17
Rationale: Explanation:
More number of days means – more length, more depth and more width. Hence, it’s a direct proportion.
(100*25*30):(75*20*50)::12:x
75000:75000::12:x
x = 12
ANSWER A
Answer: A
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $700 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $2,100 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
Options:
A)25%
B)15%
C)20%
D)40%
E)45%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 700 : 2100 -----> 1 : 3
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 4) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/4) * 100 ---> 25%
Answer : A
Answer: A
Question: A person purchased a TV set for Rs. 2700 and a DVD player for Rs. 200 . He sold both the items together for Rs. 3180. What percentage of profit did he make?
Options:
A)20%
B)6%
C)40%
D)5%
E)3%
Rationale: The total CP = Rs. 2700 + Rs. 300
= Rs. 3000 and SP = Rs. 3180
Profit(%)
= (3180- 3000)/3000 * 100
= 6%
Answer: B
Answer: B
Question: Three cubes of edges 6 cms, 8 cms and 10 cms are meted without loss of metal into a single cube. The edge of the new cube will be:
Options:
A)8 cms
B)12 cms
C)14 cms
D)16 cms
E)None
Rationale: Volume of new cube = Volume of cube 1 + cube 2 + cube 3 = 63 + 83 + 103, = 216 + 512 + 1000
a3 = 1728,
a = (1728)1/3 = 12
Answer: B
Answer: B
Question: The ratio of the ages of Maala and Kala is 1 : 4. The total of their ages is 2.0 decades. The proportion of their ages after 0.5 decades will be
[1 Decade = 10 years]
Options:
A)6:5
B)3:4
C)2:5
D)7:9
E)3:6
Rationale: Let, Maala’s age = A and Kala’s age =4A
Then A + 4A = 20
A =5
Maala’s age = 5 years
and Kala’s age = 20 years
Proportion of their ages after 5 is = (5 + 5) : (20 + 5)
= 10 : 25
= 2 : 5
Answer : C
Answer: C
Question: If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 13 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Options:
A)25 pounds
B)46 pounds
C)92 pounds
D)130 pounds
E)146 pounds
Rationale: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*13 --> x = 130.
Answer: D.
Answer: D
Question: Simple interest on a certain sum at a certain annual rate of interest is 1/4 of the sum. If the numbers representing rate percent and time in years be in the ratio 1:4, then the rate of interest is:
Options:
A)4 1/2 %.
B)3 1/2 %.
C)2 1/2 %.
D)2 3/4 %.
E)4 3/4 %.
Rationale: Explanation :
Let sum = x. Then, S.I. = x/4
Let rate = R% and time = R years.
[x * R * 4R / 100] = x / 4 ? R^2 = 25/4
R = 5/2 = 2 1/2.
Hence, R = 2 1/2 %.
Answer : C
Answer: C
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)26
B)88
C)90
D)42
E)22
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15 = Rs. 90
Answer:C
Answer: C
Question: Which of the following fraction is smallest?
Options:
A)23/28
B)14/15
C)15/19
D)21/24
E)23/25
Rationale: 23/28 =0.821
14/15 = 0.933
15/19 = 0.7894
21/24 = 0.875
So, 15/19 = 0.7894 is smallest.
ANSWER:C
Answer: C
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.2 m and its walls are 5 cm thick. The thickness of the bottom is:
Options:
A)90 cm
B)2 dm
C)1 m
D)1.1 cm
E)None of these
Rationale: Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (120 - x)] = 8000 × 1000
=> 320 × 250 × (120 - x) = 8000 × 1000
=> (120 - x) = 8000×1000/320=
100
=> x = 20 cm = 2 dm.
Answer: B
Answer: B
Question: A classroom has equal number of boys and girls. Eight girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
Options:
A)16
B)24
C)32
D)48
E)54
Rationale: after 8 girls left remaining 8 girls
now boys 16 are twice as many as remaining girls.
initially boys=16 and girls=16.
ANSWER:C
Answer: C
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony twelve hours from now?
Options:
A)77,500
B)1,860,000
C)2,480,000
D)3,720,000
E)39,680,000
Rationale: 310,000 × 2 × 2×2×2x2×2×2 = 310,000 × 128 = E
Answer: E
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 30 runs. Find his average in all the 30 matches?
Options:
A)31
B)36.67
C)88
D)13
E)12
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 300.
Total score of the batsman in the 30 matches = 1100.
Average score of the batsman = 1100/30 = 36.67.
Answer:B
Answer: B
Question: An investment yields an interest payment of $240 each month. If the simple annual interest rate is 9%, what is the amount of the investment?
Options:
A)$28,300
B)$30,400
C)$31,300
D)$32,500
E)$32,000
Rationale: Let the principal amount = P
Simple annual interest = 9%
Simple monthly interest = (9/12) = (3/4)%
(3/4)*(P/100) = 240
=>P = (240 *4 * 10^2 )/3
= 80*4*10^2
= 320 * 10^2=32000
Answer E
Answer: E
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
Options:
A)3.1
B)3.4
C)3.6
D)4
E)4.5
Rationale: 3.6
Option 'C'
Answer: C
Question: I have to run a 100 meter dash.
How many steps would I need to take if with each step i cover 20 centimeters ?
Options:
A)20
B)500
C)50
D)10
E)45
Rationale: 100centimeters=1meter
x centimeters=100meters
(20 centimeters per step) x (nos running steps)=10000 centimeters
nos running steps= 10000 centimeters /20 centimeters
500steps
The answer is B
Answer: B
Question: Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 33~ ?
Options:
A)31
B)1
C)2
D)8
E)0
Rationale: n~ = (n-1)!
so 33~ = (33-1)! = 32!
when 32!/33 we have 16*2 inside 32!
hence 33 gets cancelled and we get remainder as 0
E
Answer: E
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Options:
A)218
B)265
C)268
D)480
E)261
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48
= 480
Answer: D
Answer: D
Question: If the price of sugar rises from Rs.10 per kg to Rs. 12 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
Options:
A)17%
B)20%
C)25%
D)30%
E)none
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 10 = x × 12 = x = 83 kg.
∴ Reduction in consumption = 17%.
Answer A
Answer: A
Question: The average of 20 number is zero of them at the most, how many may be greater than zero ?
Options:
A)0
B)1
C)10
D)19
E)20
Rationale: Solution
average of 20 numbers = 0.
∴ Sum of 20 numbers = (0×20) = 0.
it is quite possible that 19 of these number may be positive and if their sum is a, then 20th number is (-a). Answer D
Answer: D
Question: The average of 35 students in a class is 16 years. The average age of 25 students is 14. What is the average age of remaining 10 students?
Options:
A)21 years
B)22 years
C)23 years
D)24 years
E)25 years
Rationale: Sum of the ages of 14 students
= (16 * 35) - (14 * 25) = 560 - 350 = 210
Required average = (210/10) = 21 years.
Answer:A
Answer: A
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Options:
A)11 days
B)66 days
C)30 days
D)77 days
E)88 days
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C
Answer: C
Question: A man rides at the rate of 40km/hr. But stops 20minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 200 kilometers?
Options:
A)5hr
B)6hr 30min
C)8hr 10min
D)7hr 20min
E)9hr
Rationale: speed of man = 40km/hr
number of rests = (200/25)-1 = 7
time taken for the man = (200/40)+7*(20/60) = 7 hr 20 min
Answer is D
Answer: D
Question: The letters U and S are rearranged to form the word 'US'. Find its probability.
Options:
A)1/4
B)1/3
C)1/2
D)1/7
E)1/5
Rationale: Explanation :
There are total 2 letters. The probability that S gets the first position is 1/2.
The probability that S is in the second position is 1/1.
Hence, the required probability is:-
=> (1/2) x 1.
=> 1/2
Answer : C
Answer: C
Question: In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/2 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
Options:
A)N/8
B)7N/8
C)11N/12
D)17N/24
E)41N/48
Rationale: The number of people who answered yes to both questions is (1/2)(1/6)N = N/12
The number of people who did not answer yes to both is 1 - N/12 = 11N/12
The answer is C.
Answer: C
Question: If n is an integer, when (2n + 2)2 is divided by 4 the remainder is
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: We first expand (2n + 2)2
(2n + 2)2 = 4n 2 + 8 n + 4
Factor 4 out.
= 4(n 2 + 2n + 1)
(2n + 2)2 is divisible by 4 and the remainder is equal to 0. The answer is A.
Answer: A
Question: Given 2x + y + z = 3 and 5x + 3y + z = 11, what is the value of x + y - z?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: (1) 5x + 3y + z = 11
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 5
The answer is C.
Answer: C
Question: A positive number x is multiplied by 2, and this product is then divided by 5. If the positive square root of the result of these two operations equals x, what is the value of x ?
Options:
A) 9/4
B) 3/2
C) 4/3
D) 2/3
E) 1/2
Rationale: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^2
3x^2 – 2x = 0
x(3x – 2) = 0
x = 0 or
3x – 2 = 0
3x = 2
x = 3/2
Because x is positive, x = 3/2. The answer is B.
Answer: B
Question: A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 85, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Options:
A)74
B)75
C)76
D)77
E)78
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 85 + 77*5x) = 260x+510x+385x = 1155x
total number of students = 15x
average = 1155x/15x = 77
D is the answer
Answer: D
Question: A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 9 less, he would have gained 25%. Find the cost price of the article.
Options:
A)150
B)160
C)170
D)180
E)360
Rationale: Let the C.P. be 100
First S.P. = 115
Second C.P. = 90
Second S.P = 125% of 90 = 112.50
Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100
But actual difference is 9.
∴ C.P. = 100⁄2.50 × 9 = 360.
Answer E
Answer: E
Question: Which of the following is equivalent to the pair of inequalities x + 8 > 10 and x - 4 <= 5 ?
Options:
A) 2 < x < 16
B) 2 <= x < 4
C) 2 < x <= 9
D) 4 < x <= 8
E) 4 <= x <= 16
Rationale: Solution:
Let’s isolate x in both inequalities, starting with x + 8 > 10.
x + 8 > 10
x > 2
Next we isolate x in the inequality x – 4  5.
x – 4 <= 5
x <= 9
Bringing these two inequalities together we know:
2 < x <= 9
The answer is C.
Answer: C
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)0
B)1
C)10
D)19
E)None
Rationale: EXPLANATION
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Answer A
Answer: A
Question: Ratio between Rahul and Deepak is 4:3, After 10 Years Rahul age will be 26 years. What is Deepak present age
Options:
A)12
B)15
C)20
D)22
E)23
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 10 = 26 => x = 4
So Deepak age is = 3(4) = 12
Answer: Option A
Answer: A
Question: The number N is 5,3H7, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
Options:
A)4
B)3
C)5
D)8
E)2
Rationale: If the number is divisible by 9, it must also be divisible by 3. Only 3 yields such a number.
Answer: B
Answer: B
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word MANGO could be arranged to create a five-letter code?
Options:
A)5!
B)5! − (3! + 2!)
C)5! − (3! × 2!)
D)5!/(3! + 2!)
E)5!/(3! × 2!)
Rationale: MANGO - five letters can be arranged in 5! ways
since there is no repetition in MANGO so
5!
Ans. A) 5!
Answer: A
Question: If x < y < 0, which of the following must be true?
Options:
A)(-x)+ (-y) is positive integer
B)2x+y is a negative integer
C)x-y is a positive integer
D)2xy/3x is a negative integer
E)xy/2
Rationale: Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
x-y is false since xSo, option A is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)
Answer : A
Answer: A
Question: The average age of a class of 22 students is 10 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)30 Years
B)31 Years
C)33 Years
D)34 Years
E)49 Years
Rationale: Total age of students is 22X10 = 220 Years
Total age inclusive of teacher = 23X (10+1) = 253
So, Teacher's age is 253-220 = 33 Yrs
There is a shortcut for these type of problems
Teacher's age is 10+(23X1) = 33 Years
C
Answer: C
Question: Given that a is the average (arithmetic mean) of the first seven positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
Options:
A)3:4
B)8:13
C)5:6
D)13:10
E)4:3
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30, 36, 42}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}
Both sets are evenly spaced, thus their median=mean:
a=24 and b=(36+42)/2=39 --> a/b=24/39=8/13.
Answer: B.
Answer: B
Question: If the sum of 9 consecutive integers is 90, what is the sum of the following 9 consecutive integers?
Options:
A)99
B)135
C)145
D)171
E)180
Rationale: 1) greatest of each will have a difference of 9 and next greatest too will have a difference of 9 and so on..
Therefore all nine terms will have a term MORE by 9..
Sum =90+(9*9)=171
2) if sum is 90, the average= median=90/9=10..The median of next 9 will be 10+9=19..
And sum would be 19*9=171
ANSWER:D
Answer: D
Question: Question:	A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $180. The cost for 1 bat and 6 balls is $190, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $195 for the purchase?
Options:
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: IMO it should be C that is C
reason:
formed an equation... bat = b ball = c
2b+4c=180
1b+6c=190
solving both we get b that is bat = 40 and c that is ball = 25
new equation 195 to be divided in equal
3b+3c=195
3*40 + 3*25 = 195
120+75= 195
Answer: C
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 18 households had a both a car and a bike and 44 had a car, how many had bike only?
Options:
A)30
B)35
C)20
D)18
E)10
Rationale: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-18+11 --> {Bike}=53 --> # those who have bike only is {Bike}-{Both}=53-18=35.
Answer: B.
Answer: B