divelab/Sys2Bench huggingface dataset:
Question: James just found out that has to work a 12 hour shift on Christmas Day, from 3pm until 3am. Since that day is a national holiday, he will get paid 2 times his normal hourly rate for the entire shift. Additionally, the state he lives in has a law that requires an overtime rate, equal to 1.5 times the shift's hourly rate, for every hour over 8 hours in one day. Finally, he will get paid a "night premium" of 20% above the shift's hourly rate for any time worked after 10pm. James' regular rate is $16 per hour. Assuming he works his full shift as scheduled, how much money will James make (before taxes) on Christmas day?
Options:
A)$460.40
B)$576.00
C)$432.00
D)$492.80
E)$518.40
Rationale: Holiday Rate calculation: Regular Hourly rate of $16 x 2 = $32 per hour
Overtime Rate calculation: Holiday shift rate $32 x 1.5 = $48 per hour
Night premium: Before 8th hour, Holiday rate $32 + 20%, calculation would be 32 x .20 = 6.4, adding 6.4 to 32 = $38.40 per hour
Night premium: After 8th hour, Holiday overtime rate $48 + 20%, calculation would be 48 x .20 = 9.6, adding 9.6 to 48 = $57.60 per hour
SHIFT HOURS BREAKDOWN:
3pm-10pm = 7 hours @ Holiday rate $32
10pm-11pm = 1 hour @ Holiday rate w/ night premium $38.40
11pm-3am = 4 hours @ Holiday Overtime rate w/ night premium $57.60
$32 x 7 = $224
$38.40 x 1 = $38.40
$57.60 x 4 = $230.40
Total for entire 12-hour shift, pre-taxes: $492.80
Answer: D
Question: Shop Offered 25% offer for every Shirt, Smith bought a shirt at Rs. 560. and What was the shop's original selling Price?
Options:
A)500
B)550
C)746
D)700
E)750
Rationale: SP* (75/100) = 560
SP= 7.46 * 100 => CP = 746
Answer:C
Answer: C
Question: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.05, what is value of J?
Options:
A)22
B)56
C)280
D)112
E)175
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.08, the decimal part of the decimal quotient, must equal the remainder, 14, divided by the divisor J.
0.05 = 14/J
0.05*J = 14
J = 14/0.05 = 1400/5 = 280
So J = 280, answer = C.
Answer: C
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts four hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
Options:
A)3
B)4.5
C)8
D)d) 5.5
E)e) 5
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 4+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(4+T) = 40*T
T = 12 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*12/60 = 8 hrs
Time taken by A = 4+T = 4+12 = 16 hrs
Time taken by K = 8 hrs
So K starts 16-8 = 8 hrs after A. (answer C)
Answer: C
Question: Find the compound interest and the amount on Rs.3000 at 5% per annum for 3 years when C.I is reckoned yearly?
Options:
A)s.261.88
B)s.440.88
C)s.472.88
D)s.346.88
E)s.446.88
Rationale: A = 3000(21/20)3
= 3472.88
= 3000
---------
472.88
ANSWER:C
Answer: C
Question: How many three-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
Options:
A)85
B)90
C)95
D)100
E)105
Rationale: N=(4*5-1)*5*=85
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 44 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
A
Answer: A
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length W of the fence including the fence posts on each end?
Options:
A)mn
B)m(n + x)
C)W=m(n + x) + x
D)m(n + x) + 2x
E)2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.
The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: C
Question: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/25, then the reciprocal of n must be
Options:
A)Less than -5
B)Between -1 and -1/5
C)Between -1/5 and 0
D)Between 0 and 1/5
E)Greater than 5
Rationale: n^2 < 1/25
abs(n) < 1/5
Since n<0, then 0 > n > -1/5
1/n < -5
The answer is A.
Answer: A
Question: A rainstorm increased the amount of water stored in State J reservoirs from 130 billion gallons to 160 billion gallons. If the storm increased the amount of water in the reservoirs to 80 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
Options:
A)75
B)70
C)65
D)85
E)90
Rationale: Let total capacity be x
we know 160 = 0.80x
x = 160/0.80 = 200
Prior to storm, we had 130 bn gallons
200-130 = 70
Answer : B
Answer: B
Question: In a office work is distribute between p persons. If 1/7 members are absent then work increased for each person is?
Options:
A)13.67%
B)14.67%
C)15.67%
D)16.67%
E)17.67%
Rationale: let total % of work is 100%
total person=p
1/7 person are absent of total person . so absent person is 1/7p ie p/7.
left person is, p-p/7=6p/7.
p person do the work 100%
1 person do the work 100*p%
6p/7 person do the work (100*p*7)/6p%=116.67%
work increased for each person is=(116.67-100)%=16.67%
ANSWER:D
Answer: D
Question: Two persons start running simultaneously around a circular track of length 500 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)11
B)10
C)28
D)45
E)12
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 500 / (15 + 25)5/18 = 500* 18 / 40 * 5 = 45 seconds.
Answer: D
Answer: D
Question: A certain telescope increases the visual range at a particular location from 80 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?
Options:
A) 30%
B) 33 1/2%
C) 40%
D) 60%
E) 87.5%
Rationale: Original visual range = 80 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-80)/80 * 100%
= 7/8 * 100%
= 87.5 %
Answer E
Answer: E
Question: The volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 5. What is the length of the wire?
Options:
A)A)5:4
B)B)2:7
C)C)2:2
D)D)2:1
E)E)2:9
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/20 = (1)2h1/(5)2h2
=> h1/h2 = 5/4
i.e. h1 : h2 = 5 : 4
Answer: A
Answer: A
Question: A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have ?
Options:
A)1000
B)1074
C)1075
D)1080
E)1089
Rationale: Explanation:
No. of digits in 1-digit page nos. = 1x9 = 9.
No. of digits in 2-digit page nos. = 2 x 90 = 180.
No. of digits in 3-digit page nos. = 3 x 900 = 2700.
No. of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
Therefore No. of pages with 4-digit page nos. = (300/4) = 75.
Hence, total number of pages = (999 + 75) = 1074.
Answer: B
Answer: B
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
Options:
A)12%
B)12.5%
C)13%
D)14%
E)14.5%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
B)
Answer: B
Question: What is cost price of an article sold by a trader at 15% loss, given that the trader would have made a profit of 6% if he had sold it for $30 more?
Options:
A)$576.19
B)$436.19
C)$476.19
D)$470.19
E)$276.19
Rationale: Let C.P. be $x
Then 106% of x - 85% of x = 100
21% of x = 100
21/100 *X = 100
21x = 10000
x = 476.19
Answer is C
Answer: C
Question: Mangala completes a piece of work in 20 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)12 days
C)14 days
D)16 days
E)18 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 20 × 30/50 = 12 days
B
Answer: B
Question: If the terms of a series are either2or24and the sum of all the terms F of the series is 124, then which of the following could be the number of2sin the series?
Options:
A)26
B)29
C)35
D)40
E)48
Rationale: Ans: A
Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms F is 124 means 24*5= 120 so number of 24 can't be more than 5
so 24x +2y = 124
24*5 + 2y =124 then y=2
24*4 + 2y = 124 then y=14
24*3 +2y = 124 then y= 26
24*2 +2y =124 then y = 38
24 +2y = 124 then y= 50
26 is the ans.A
Answer: A
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is
Options:
A)45
B)50
C)55
D)60
E)65
Rationale: Option A
Answer: A
Question: In the rectangular coordinate system, if the line x = 4y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
Options:
A)3
B)2
C)1/2
D)1/3
E)1/4
Rationale: x = 4y+5, and thus y = x/4 - 5/4
The slope is 1/4.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/4 and thus p = 1/2
The answer is C.
Answer: C
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 14 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
Options:
A)2,000
B)5,000
C)10,000
D)35,000
E)52,000
Rationale: out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
14 broken glass will be from 35000 bulbs
Answer is D
Answer: D
Question: Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 10 years older than Larry, how old is Annie?
Options:
A)3
B)8
C)19
D)26
E)34
Rationale: J = L+10
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+15
Let's subtract equation (1) from equation (2)
A+9 = 12
A = 3
The answer is A.
Answer: A
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)287 m
B)350 m
C)267 m
D)287 m
E)656 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer:B
Answer: B
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
Options:
A)100
B)110
C)128
D)134
E)156
Rationale: First Purchased = 250 Wes= 128
C
Answer: C
Question: The mean proportional between 4 and 16 is?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: root of(4*16)=2*4=16
ANSWER:E
Answer: E
Question: In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what X percentage of those asked favoured more than one of the 3 proposals.
Options:
A) 10
B) 12
C) 17
D) 22
E) 30
Rationale: Bunuel, my answer for exactly 2 people was 17 and this was my approach:
100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to
X=100%=(50+30+20)-(at least 2 people)-5%+22%.C
Answer: C
Question: The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
Options:
A)3
B)5
C)7
D)11
E)13
Rationale: x + y = 25
xy = 144
(x- y)2 = (x + y)2 – 4xy
(x- y)2 = 625 – 576 => (x – y) = 7
ANSWER:C
Answer: C
Question: Max owns 200 shares of stock A and 180 of stock b. Last month the stocks had gained and lost the amounts shown below. What was Max's net gain or loss for the month?
Stock Gain/Loss
A 200 -18
B 180 40
Options:
A)3600
B)-3600
C)7200
D)10800
E)438
Rationale: Find how much the gain or loss is and add all stocks together in the end.
Correct answer is A)3600
Answer: A
Question: A can run 4.5 km distance in 1 min 30 seconds, while B can run this distance in 3 min. By how much distance can A beat B?
Options:
A)2250 m
B)1000 m
C)1250 m
D)1800 m
E)2000 m
Rationale: A takes time 1.30 minutes=90 sec
B takes time 3 minutes=180sec
diffrence= 180-90=90sec
now we are to find distance covered in 90 sec by B
180sec=4500m
1sec=25m
90sec=25x90=2250m
ANSWER:A
Answer: A
Question: Which of the following equations describes a line that is perpendicular to y=x+4?
Options:
A)y = x − 4
B)y = −2 − x
C)y = 4x
D)y = 4x+1
E)y = 1/x + 4
Rationale: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y=x+4 is 1 so the slope of a perpendicular line will be -1.
The answer is B.
Answer: B
Question: The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 5 years ago, the sum of their ages was 75, what will be the age of Aman 10 years from now?
Options:
A)17
B)25
C)27
D)35
E)40
Rationale: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.
5x-5 + 8x-5 + 7x-5 = 75
x = 3
Present age of Aman = 5*3 = 15
Aman's age 10 years hence = 15+10 = 25
Answer = B
Answer: B
Question: A man borrowed Rs.10000 from a lender at 9% p.a rate of interest. Find the amount to be paid by the man after 2years 6months?
Options:
A)Rs 10050
B)Rs 12050
C)Rs 12250
D)Rs 13000
E)Rs 14550
Rationale: Principal = Rs 10000 Rate of interest R = 9%
T= 2 years 6 months= 2 ½ years=
5/2 years
Simple Interest=
PTR/100
= 10000 X
5/2 X 9/100
= Rs 2250
Amount= Prinipal + Simple interest = Rs 10000+ Rs 2250 = Rs 12250 C)
Answer: C
Question: The amount of water (in ml) that should be added to reduce 18 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
Options:
A)8 ml
B)5 ml
C)4 ml
D)6 ml
E)12 ml
Rationale: 9 9
30% 70%
30% ----- 9
70% ------? => 21 - 9 = 12 ml
Answer:E
Answer: E
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
Options:
A)5/17
B)5/12
C)1/98
D)2/08
E)3/76
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: B
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage?
Options:
A)80%
B)50%
C)75%
D)40%
E)53%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 175 (35 * 5)
Profit percentage
= (175 - 100)/100 * 100 = 75%
Answer: C
Answer: C
Question: If Tim had lunch at $50.50 and he gave 10% tip, how much did he spend?
Options:
A)A)$57.45
B)B)$35.42
C)C)$60.60
D)D)$55.55
E)E)$78.45
Rationale: The tip is 10% of what he paid for lunch.
tip = 10% of 50.50 = (10/100)*50.50 = $5.05
Total spent
50.50 + 5.05 = $55.55
correct answer is D)$55.55
Answer: D
Question: Two pipes can fill a tank in 15 hours and 30 hours. While the 3rd pipe empties the full tank in 45hours. If all the 3 pipes are open in how much time will the tank be filled?
Options:
A)15/72
B)88/12
C)75/16
D)90/11
E)57/10
Rationale: Net part filled in 1 hour = 1/15 + 1/30 - 1/45 = 11/90
The tank will be full in 90/11 hr
Answer is D
Answer: D
Question: Cara and Dan drive at constant speeds toward each other on a highway. Cara drives at a constant speed of 32 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Cara is 110 km away from Dan at 7 am, and also 110 km away from Dan at 11 am, then how fast is Dan driving (in kilometers per hour)?
Options:
A)20
B)23
C)26
D)29
E)32
Rationale: Cara and Dan complete 220 km / 4 hours = 55 km/hour
Dan's speed is 55-32=23 km/hour
The answer is B.
Answer: B
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
A)3/140
B)1/28
C)3/56
D)3/35
E)7/40
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.
Answer: E.
Answer: E
Question: Of the 3,600 employees of Company X, 16/25 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
Options:
A)57%
B)22.2%
C)20%
D)12.5%
E)11.1%
Rationale: Let's see, the way I did it was
16/25 are clerical out of 3600 so 2304 are clerical
2304 reduced by 1/4 is 2304*1/4
so it reduced 576 people , so there is 1728 clerical people left
but since 576 people left, it also reduced from the total of 3600 so there are 3024 people total
since 1728 clerical left / 3024 people total
you get (A) 57%
Answer: A
Question: What is the probability of getting at least one six in a single throw of three unbiased dice ?
Options:
A)31/216
B)91/216
C)125/216
D)81/216
E)81/359
Rationale: Explanation :
Three cases arise:
Case 1: When only one dice shows up a six
This dice can be any of the 1st, 2nd or 3rd dice. Find the probability for these three independent events and add them up to get the total probability
Probability that only 1st dice shows up a six: (probability that first dice shows up a 6) and (probability that second dice shows up other than 6) and (probability that third dice shows up other than 6)
=(1/6)*(5/6)*(5/6)
=25/216
similarly probability that 2nd dice shows up a six: (5/6)*(1/6)*(5/6) = 25/216
And, probability that 3rd dice shows up a six: (5/6)*(5/6)*(1/6) = 25/216
So probability that only one dice shows up a six: (25/216)+(25/216) +(25/216) = 75/216
Case 2:When two dice show up a six
Total number of ways of selecting a pair of dice that show up a six from a set of 3 dice are: 3C2=3
Find the probability of getting six on a pair of dice and multiply it by total number of such possible pairs
Probability of getting a six on a pair of dice = (1/6)*(1/6)*(5/6) = 5/216
So, total probability = 3*(5/216) = 15/216
Case 3: When all dice show up a six
In this case total probability is just (1/6)*(1/6)*(1/6) = 1/216
So total probability of getting at least one six = (75/216) + (15/216) + (1/216) = 91/216
Answer : B
Answer: B
Question: An advertising agency finds that, of its 180 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
Options:
A)56
B)70
C)90
D)98
E)80
Rationale: Total=180
Television=115
Radio=110
Magazine=130
All the three =180-115-110-130+85+75+95=80
ANSWER E
Answer: E
Question: 30 is subtracted from 40% of a number, the result is 50. Find the number?
Options:
A)200
B)997
C)266
D)288
E)271
Rationale: (40/100) * X – 30 = 50
4X = 800
X = 200
Answer:A
Answer: A
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Options:
A)125/127
B)127/125
C)125/126
D)126/125
E)126/127
Rationale: Required probability = 1 - 1/126 = 125/126
Answer: C
Answer: C
Question: A retailer bought a machine at a wholesale price of $99 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?
Options:
A)81
B)100
C)120
D)132
E)160
Rationale: My solution: Wholesale Price= 99
Retail Price, be = x
He provides 10 % discount on Retail price= x-10 x/100
This Retail price = 20 % profit on Wholesale price
x-10 x/100 = 99+ 1/5(99)
x=132;
ANSWER:D
Answer: D
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
A)8/3
B)3/8
C)8/5
D)12/5
E)5/3
Rationale: Distance traveled by Eddy = 540 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 540/3 = 180 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 180/75 = 12/5
Answer D
Answer: D
Question: A group of 10 representatives is to be selected out of 16 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
Options:
A)16C₅ * 10
B)16C₇ * 10
C)16C11 * ¹⁰C₅
D)12 * ¹⁰C₅
E)None of these
Rationale: Here, five seniors out of 16 seniors can be selected in 16C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 16C₅ * ¹⁰C₅ = 16C11 * ¹⁰C₅
since 16C₅ = 16C11
ANSWER:C
Answer: C
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
Options:
A)3:4:6
B)3:4:7
C)3:4:0
D)3:4:2
E)3:4:1
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7.
Answer: B
Answer: B
Question: The difference between the place value and the face value of 6 in the numerical 856973 is
Options:
A)973
B)6973
C)5994
D)9554
E)None of them
Rationale: =(place value of 6)-(Face value of 6)
=(6000-6)
=5994
Answer is C
Answer: C
Question: In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?
Options:
A)24
B)48
C)56
D)72 ways
E)96
Rationale: These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
ANSWER:D
Answer: D
Question: A car is running at a speed of 90kmph. What distance will it cover in 10sec?
Options:
A)100m
B)150m
C)180m
D)200m
E)250m
Rationale: Speed = 90kmph = 90*5/18 = 25 m/s
Distance covered in 10sec = 25*10 = 250m
Answer is E
Answer: E
Question: The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.
Options:
A)28 and 17
B)27 and 18
C)25 and 15
D)27 and 15
E)25 and 18
Rationale: Let the number be x and y. Then,
x – y = 11 ----(i) and 1/5 (x + y) = 9 => x + y = 45 ----(ii)
Adding (i) and (ii), we get: 2x = 56 or x = 28. Putting x = 28 in (i), we get: y = 17.
Hence, the numbers are 28 and 17.
Answer is A.
Answer: A
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 9?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?
Options:
A)25x^2 + 4 = y^2
B)75x^2 = 3y^2 - 12
C)25x^2 = (y + 2)(y - 2)
D)5x = y - 2
E)5x = y - 3
Rationale: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 3
If we square both sides, we end up with....
(5X)^2 = (Y-3)^2
(5X)(5X) = (Y-3)(Y-3)
25X^2 = Y^2 - 6Y + 9
This is NOT a match for the original equation, so it's the answer that is NOT equivalent. E
Answer: E
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 year?
Options:
A)306.06
B)306.02
C)306.04
D)306.09
E)306.12
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer: C
Answer: C