divelab/Sys2Bench huggingface dataset:
Question: The area of a square is equal to seven times the area of a rectangle of dimensions 25 cm * 343 cm. What is the perimeter of the square?
Options:
A)810 cm
B)800 cm
C)980 cm
D)718 cm
E)860 cm
Rationale: Area of the square = s * s = 7(343 * 25)
=> s = 5 * 7 * 7 = 245 cm
Perimeter of the square = 4 * 245 = 980 cm.
Answer: C
Answer: C
Question: A cistern is normally filled in 4 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options:
A)33
B)88
C)40
D)99
E)12
Rationale: 1/4 - 1/x = 1/6
x = 12
Answer: E
Answer: E
Question: If c^2 = d^2, which of the following must be true?
Options:
A)c = d
B)|c| = |d|
C)c = |d|
D)c = −|d|
E)c=-d
Rationale: Since c^2=d^2 we have 0=c^2 – d^2 =(c-d)*(c+d). So c=d or c=-d.
So only (A) and only (E) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (D) tells us that k should be less than or equal to 0.
So neither (C) nor (D) cannot be the answer.
The answer is, therefore, (B).
Answer: B
Question: Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
Options:
A)120
B)126
C)252
D)1200
E)1260
Rationale: My ans is 10C3 = 120
A
Answer: A
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)Rs.10000
B)Rs.12800
C)Rs.6000
D)Rs.8000
E)Rs.13000
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
ANSWER:B
Answer: B
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.5, what is the probability that Malachi will return home at the end of the day on the following Monday?
Options:
A)0.008
B)0.125
C)0.128
D)0.512
E)0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.5
Therefore, probability of no rain = 0.5
0.5*0.5*0.5 = 0.125
Hence B
Answer: B
Question: If 12 : 18 :: x : 9, then find the value of x
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Explanation:Treat 12:18 as 12/18 and x:9 as x/9, treat :: as = So we get 12/18 = x/9=> 18x = 108=> x = 6 Option C
Answer: C
Question: A reduction of 21% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Options:
A)s.2.66
B)s.2.4
C)s.2.5
D)s.2.2
E)s.2.1
Rationale: 100*(21/100) = 21 --- 10
? --- 1 => Rs.2.1
100 --- 79
? --- 2.1 => Rs.2.66
Answer:A
Answer: A
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)7
B)8
C)9
D)6
E)2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: B
Question: The product of x and y is a constant. If the value of x is increased by 50%, by what percentage must the value of y be decreased?
Options:
A)50%
B)40%
C)33 1⁄3%
D)25%
E)12 1⁄2%
Rationale: Product of x and y = xy
If the value of x is increased by 50% , value of y needs to be = xy/(1.5 x ) = 2/3 y
Decrease in value of y = y - 2/3 y = 1/3 y
% decrease in value of y = (1/3 y)/y * 100%
=33 1⁄3%
Answer C
Answer: C
Question: The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is?
Options:
A)50
B)80
C)100
D)110
E)130
Rationale: Let the number of candidate who passed = y
Then, 39y + 15(120 - y) =120 x 35
⇒ 24y= 4200 -1800
∴ y= 2400 / 24 = 100
C
Answer: C
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,710 minutes earlier? (Assume standard time in one location.)
Options:
A)6:22
B)6:24
C)6:27
D)6:30
E)6:32
Rationale: 6:27minus 2,880,710in any way must end with 7, the only answer choice which ends with 7 is C.
Answer: C.
Answer: C
Question: The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.60 per metre.
Options:
A)2399
B)3888
C)2999
D)5808
E)6072
Rationale: Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.60) = Rs. 6072.
Answer: E) 6072
Answer: E
Question: The average of five results is 46 and that of the first four is 45. The fifth result is?
Options:
A)50
B)88
C)77
D)66
E)51
Rationale: 5 * 46 – 4 * 45
= 50
Answer: A
Answer: A
Question: By selling a house for Rs.45000, it was found that 1/2 of the outlay was gained, what ought the selling to price to have been in order to have lost 2 p.c?
Options:
A)38020
B)38000
C)38028
D)29400
E)38192
Rationale: CP + CP/2 = 45000
CP = 30000
SP = 30000*(98/100)
=29400
Answer:D
Answer: D
Question: A is a set containing 8 different positive odd numbers. B is a set containing 7 different numbers, all of which are members of A. Which of the following statements CANNOT be true?
Options:
A)The range of B is even.
B)The mean of A is even.
C)The mean of B is even.
D)The range of A is equal to the range of B.
E)The median of B is equal to the mean of B.
Rationale: Given: A is a set containing 8 different positive odd numbers
Easily inferred: B is a set containing 7 differentoddnumbers
(A) The range of B is even. - Always even, since it is a difference of two odd numbers
(B) The mean of A is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of B is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of A is equal to the range of B.
(E) The median of B is equal to the mean of B
Option C.
Answer: C
Question: Find unit digit of N when N = 63^1!+2!+...+63! + 18^1!+2!+...+18! + 37^1!+2!+...37!
Options:
A)2
B)4
C)6
D)8
E)0
Rationale: 3,8 and 7 have a power cycle of 4, i.e. the units digit in each case will repeat after every 4th power.
For eg : 3^1 = 3, 3^2 = 9 , 3^3 = 27 , 3^4 = 81, 3^5 = 243
All the powers given(1!+2!+....), are multiples of 4. It is so because the last 2 digits of the total sum will be 00,for each one of them, which make them divisible by 4.
Thus, the given problem boils down to 3^4+8^4+7^4=1+6+1=8
Thus, the units digit is 8.
ANSWER:D
Answer: D
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (4/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
Options:
A) 2/5
B) 1/2
C) 11/16
D) 5/7
E) 3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 4/8*c:
(b+c)/2 = (4/8)*c
b = 0
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (0)/2 = 0
Median = (a + c)/2 = (0 + c)/2 = c/2 = (1/2)*c (ANSWER B)
Answer: B
Question: The average height of 50 pupils in a class is250 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is __________ .
Options:
A)151 cm
B)351 cm
C)241 cm
D)251 cm
E)261 cm
Rationale: Total height = 250 * 50 = 12500 cm.
New average = [12500 - 5 * 146 + 5 * 156 ] / 50 =251 cm.
ANSWER:D
Answer: D
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
Options:
A)20 years
B)17 years
C)97 years
D)27 years
E)29 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer: A
Answer: A
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Options:
A)84 degrees
B)64 degrees
C)54 degrees
D)44 degrees
E)24 degrees
Rationale: Explanation:
Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 8 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 8 or x = 8.
Temperature on the 5th day = 8x = 64 degrees.
Answer: B
Answer: B
Question: In how many years will a sum of money double itself at 10% per annum?
Options:
A)2 years 4 months
B)4 years 2 months
C)8 years 4 months
D)10 years 8 months
E)None
Rationale: Sol.
Let sum = x. Then, S.I. = x
∴ Time = [100 * S.I. / P*R] = [100 * x / x * 12] years
= 8 1/3 years = 8 years 4 months.
Answer C
Answer: C
Question: A certain car averages 35 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
Options:
A)28
B)30
C)33
D)39
E)38
Rationale: Answer D
No of Miles per Gallon = Total no of miles/Total no of Gallons
=10+50/(10/35+50/40) ~ 39.06
Answer: D
Question: Two trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9 sec
B)10.1 sec
C)10.6 sec
D)11.88 sec
E)10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 190 = 330 m.
Required time = 330 * 9/250
= 11.88 sec.
Answer:D
Answer: D
Question: A 12% stock yielding 10% is quoted at:
Options:
A)223
B)2778
C)277
D)120
E)288
Rationale: Explanation:
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 12, money invested = = Rs. 120.
Market value of Rs. 100 stock = Rs. 120.
Answer: D) 120
Answer: D
Question: What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?
Options:
A)1/6
B)1/4
C)1/2
D)21/216
E)32/216
Rationale: The other way would be to list out each option.
The options for a sum of 8: (6,1,1) has 3 options ie (6,1,1), (1,6,1), (1,1,6); (5,2,1) has 6 options, (4,3,1) has 6 options, (4,2,2) has 3 options, (3,3,2) has 3 options. We have 21 options to get 8.
The options for a sum of 14: (6,4,4) has 3 options, (6,5,3) has 6 options, (6,6,2) has 3 options, (5,5,4) has 3 options. We have 15 options to get 14.
Total: 21+15= 36/216 = 1/6.
Answer A.
Answer: A
Question: When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $109.90, what was the total value of the item?
Options:
A)$1940
B)$2150
C)$2360
D)$2570
E)$2780
Rationale: Let x be the value of the item.
0.07*(x-1000) = 109.90
x = 2570
The answer is D.
Answer: D
Question: From a group of 17 astronauts that includes 8 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
Options:
A)248
B)258
C)268
D)278
E)288
Rationale: number of astronauts with previous experience = 8
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group
(8C1)*(9C2)
=8*36= 288
Answer : E
Answer: E
Question: At a local supermarket, a box of cereal usually costs 5 dollars. This week, the supermarket sells the box of cereal for 3 dollars. How much money will you save if you buy this cereal at this supermarket?
Options:
A)5 dollars
B)3 dollars
C)4 dollars
D)2 dollars
E)1 dollar
Rationale: Solution:
In this situation, there is a decrease in the price.
Saving = 5 - 3 = 2 dollars
Option D
Answer: D
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 39000, then the share of B is?
Options:
A)18000
B)24000
C)24005
D)24009
E)24002
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 39000
Share of B = 6/13 (39000) = Rs. 18000
Answer: A
Answer: A
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 7 questions. If each question has 5 answer choices, and Kim answers every question, in how many different ways can she complete the test?
Options:
A)a 40
B)b 400
C)c 5^8
D)d 8^5
E)e 5^7
Rationale: different ways to solve each question is 5.
So, 5*5*5*5.. 7 times ----> 5^7
Answer will be E
Answer: E
Question: David walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 2 hours . He would have gained 1 hour by driving both ways. How long would it have taken for him to walk both ways.
Options:
A)3 h
B)3 h 15 min
C)4 h
D)5 h
E)6 h
Rationale: 1.Walking to to a viewpoint+Driving back=2 hours
2.Driving to a viewpoint+Driving back=2 hours - 1 hour=1 hour,
thereforeone way driving=1 hour/2 = 30 minutes.
3. From 1.one way driving=2 hours-30 minutes=1 hour 30 minutes.
4.Walking to to a viewpoint+Walking back=1 hours 30 minutes+1 hours 30 minutes=3 hours
Answer: A
Answer: A
Question: 8.5 × 6.4 + 4.5 × 11.6 = ? ÷ 4
Options:
A)426.2
B)426.4
C)106.6
D)422.4
E)522.5
Rationale: Explanation:
(54.4+52.2) × 4 = 426.4
Answer: Option B
Answer: B
Question: In the xy-plane, line w passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line w?
Options:
A)3x+2y-5=0
B)3x+2y+5=0
C)2x-3y-12=0
D)2x+3y=0
E)4x+3y-6=0
Rationale: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line w should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.
Answer: A
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and returning each hat before taking out the next one?
Options:
A)1/8
B)1/4
C)1/2
D)3/8
E)7/12
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue.
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C3 = 4 such cases so we need to multiply this by 4.
P(exactly 3 red hats) = 4*1/16 = 1/4
Clearly the probability of getting exactly 3 blue hats will also be 1/4.
The sum of the probabilities is 1/4+1/4 = 1/2
The answer is C.
Answer: C
Question: Kelvin earns $60 a week from his job. His income increased and now makes $70 a week. What is the percent increase?
Options:
A)16.66%
B)18%
C)18.2%
D)19.3%
E)20%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
A
Answer: A
Question: A bank offers 3% compound interest calculated on quarter-yearly basis. A customer deposits $ 15000 each in 1st month. At the end of the year, the amount he would have gained by way of interest is?
Options:
A)200
B)150
C)455
D)300
E)600
Rationale: Amount = (15000)* (1 + (3/4*100))^4
Amount = 15000 * (1+ 0.0075)^4 = 15455 ------(for investment in 1st month)
Interest = 15455-15000 = 455..............
Ans -C
Answer: C
Question: Seven years ago the average age of a family of 2 members was 21 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
Options:
A)10years
B)13years
C)15years
D)17years
E)20years
Rationale: Explanation:
Average of the family of two numbers
7 years ago = 21
= (21+ 7) * 2 = 56 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 - 56 = 13 years
Answer: Option B
Answer: B
Question: By selling 100 pencil, a trader gains the cost of 33 Pencil. Find his gain percentage?
Options:
A)26 1/3%
B)51 1/3%
C)33 %
D)53 1/3%
E)34 1/3%
Rationale: C
33 %
Let the CP of each pencil be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 33 pencil = Rs. 33
Profit% = 33/100 * 100 = 33 %
Answer: C
Question: If a quarter kg of onions costs 40 paise, how many paise will 100 gm cost?
Options:
A)32 paise
B)65 paise
C)56 paise
D)87 paise
E)16 paise
Rationale: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 40 : x
250 * x = (100 * 40)
x = (100 * 40) / 250
x = 16
ANSWER: E
Answer: E
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)4 min
B)5 min
C)6 min
D)8 min
E)10 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
ANSWER A
Answer: A
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 10
Options:
A)5/13
B)2/15
C)1/12
D)3/17
E)6/19
Rationale: Total number of cases = 6*6 = 36
Favourable cases = [(5,6)(6,5),(6,6)] = 3
So Probability = 3/36 = 1/12
Answer is C
Answer: C
Question: The speeds of three motor bikes are in the ratio 24 : 4 : 6. The ratio between the time taken by them to travel the same distance is :
Options:
A)1 : 4 : 4
B)1 : 6 : 3
C)1 : 6 : 5
D)1 : 6 : 4
E)1 : 5 : 4
Rationale: Ratio of time taken :
1/24 :1/4 : 1/6 = 1 : 6 : 4
ANSWER:D
Answer: D
Question: Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34, 42}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}
Options:
A) I only
B) III
C) IIII
D) IIIII
E) I, II,III
Rationale: (1)	Multiplying all the numbers change Standard Deviation
(2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number there in the Set Q.
Set II: elements are multiplied by 2 and standard deviation changes.
Hence the answer is E.
Answer: E
Question: Jamboree and GMAT Club Contest Starts
QUESTION #10:
How many words (with or without meaning)Q can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
Options:
A) 660
B) 600
C) 500
D) 300
E) 240
Rationale: In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical. in this case,Q if you think logically, A,B,C,D options are not divisible by 6!. 6 is total number of letters in the word SELFIE. Only option E is divisible by 6!. So correct answer is E that is 240
Answer: E
Question: The perimeters of two squares are 48 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
Options:
A)76 cm
B)35.6 cm
C)88 cm
D)55 cm
E)34 cm
Rationale: We know perimeter of square = 4(side)
So Side of first square = 48/4 = 12 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 12*12 - 8*8
= 80 cm
So side of third square = 8.9 [because area of square = side*side]
Perimeter = 4*Side = 4*8.9 = 35.6 cm
Answer:B
Answer: B
Question: All but one of the following statements are definitely true, identify the false statement, given that V is the brother of W and X. Y is V's son and Z is W's son?
Options:
A)V is Z's uncle
B)W is Y's uncle
C)X is Y's uncle
D)X is Y's brother
E)Y is Z's nephew
Rationale: Explanation:
All the statements are true except D (X is Y's brother), Y is V's son that makes X his uncle, not brother.
Answer: D)
Answer: D
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Options:
A)22
B)89
C)277
D)278
E)291
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer: B
Answer: B
Question: The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Options:
A)10 d
B)0 d
C)15 d
D)5 d
E)20 d
Rationale: Angle traced hr 13/3 = (360/12 * 13/3) = 130
traced by min hand 20 min = (360/60*20) = 120
req = (130-120) = 10 d
ANSWER A
Answer: A
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many E ways can the assembly line be arranged?
Options:
A)120
B)240
C)360
D)480
E)720
Rationale: C) 360
short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want E=6C!/2 -> 720/2 = 360
Answer: C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds, is
Options:
A)200 m
B)225 m
C)245 m
D)250 m
E)None
Rationale: Sol.
Speed = [45x5/18] m/sec = (25/2)m/sec; Time = 30 sec.
Let the length of bridge be x metres.
Then, 130 + x / 30 = 25 / 2
⇔ 2(130 + x) = 750
⇔ x = 245 m.
Answer C
Answer: C
Question: If d > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - d) =
Options:
A)1/4
B)1/3
C)1/2
D)3/4
E)1
Rationale: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have d-x=2t. So y-x=-t, y-d=-3t. ---> (y - x)/(y - d) = 1/3.
The answer is (B).
Answer: B
Question: If 16% of 40% of a number is 7, then the number is
Options:
A)200
B)225
C)109.375
D)320
E)None of these
Rationale: Explanation:
Let 16/100×40/100×a=7
a = 7×100×100/16×40=109.375
Correct Option: C
Answer: C
Question: In how many ways can a group of 3 men and 3 women be made out of a total of 7 men and 4 women?
Options:
A)163
B)167
C)130
D)174
E)180
Rationale: We need to select 3 men from 7 men and 3 women from 4 women. Number of ways to do this= 7C3 × 4C3130C)
Answer: C
Question: Integers 3n+2 and 8n+6 are divisible by an integer p. If p is not equal to 1, then p equals to?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: If p divides 3n+2, then p divides 24n+16.
If p divides 8n+6, then p divides 24n+18.
Then p must equal 2.
The answer is A.
Answer: A
Question: The units digit of (10)^(87) + (93)^(46) is:
Options:
A)9
B)4
C)6
D)8
E)0
Rationale: first part will be zero always
2nd part with power of three
Therefore, the second term has a units digit of 9.
Of course 0 + 9 = 9,
A
Answer: A
Question: one man can do a piece of work in 10days. one boys join him & he complete the work in 6days . if he gets 50rs for his work then what will be the share of the boy.
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: 1 day work of Man=1/10, If Boy's 1 day work=1/x, then
(1/10)+(1/x)=1/6, x=15
Ratio of work of Man & Boy=1/10:1/15=3:2
So out of 50 Rs. Boy's share=2*50/(3+2)=20
ANSWER:B
Answer: B
Question: The perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)87 cm2
B)28 cm2
C)98 cm2
D)26 cm2
E)55 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 44/2
= 55 cm2
Answer:E
Answer: E