UPSC Insta–DART (Daily Aptitude and Reasoning Test) 9 Aug 2024
Kartavya Desk Staff
Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too. We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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• Question 1 of 5 1. Question The watchman at three different places on the ground blow a whistle after every 42 sec, 60 sec, and 78 sec respectively. If they all blow the whistle simultaneously at 9:30:00 hours, then at what time do they whistle again together. a) 11:01:00 hours. b) 10:01:00 hours c) 01:01:00 hours d) 12:01:00 hours Correct Answer: (a) 11:01:00 hours Explanation: They all will whistle again at the same time after an interval that is equal to the LCM of their individual whistle-blowing cycles. So, LCM (42, 60, 78) = 2 3 7 10 13 = 5460 Therefore, they will blow the whistle again simultaneously after 5460 sec, i.e., after 1 hour 31 minutes, i.e., at 11:01:00 hours. Incorrect Answer: (a) 11:01:00 hours Explanation: They all will whistle again at the same time after an interval that is equal to the LCM of their individual whistle-blowing cycles. So, LCM (42, 60, 78) = 2 3 7 10 13 = 5460 Therefore, they will blow the whistle again simultaneously after 5460 sec, i.e., after 1 hour 31 minutes, i.e., at 11:01:00 hours.
#### 1. Question
The watchman at three different places on the ground blow a whistle after every 42 sec, 60 sec, and 78 sec respectively. If they all blow the whistle simultaneously at 9:30:00 hours, then at what time do they whistle again together.
• a) 11:01:00 hours.
• b) 10:01:00 hours
• c) 01:01:00 hours
• d) 12:01:00 hours
Answer: (a) 11:01:00 hours
Explanation:
They all will whistle again at the same time after an interval that is equal to the LCM of their individual whistle-blowing cycles. So, LCM (42, 60, 78) = 2 3 7 10 13 = 5460 Therefore, they will blow the whistle again simultaneously after 5460 sec, i.e., after 1 hour 31 minutes, i.e., at 11:01:00 hours.
Answer: (a) 11:01:00 hours
Explanation:
They all will whistle again at the same time after an interval that is equal to the LCM of their individual whistle-blowing cycles. So, LCM (42, 60, 78) = 2 3 7 10 13 = 5460 Therefore, they will blow the whistle again simultaneously after 5460 sec, i.e., after 1 hour 31 minutes, i.e., at 11:01:00 hours.
• Question 2 of 5 2. Question Find the least number which when divided by 6,7,8 leaves a remainder of 3, but when divided by 9 leaves no remainder. a) 121 b) 171 c) 131 d) 161 Correct Answer: (b)171 Explanation: LCM (6, 7, 8) = 168 So the number is of the form 168m + 3 Now, 168m + 3 should be divisible by 9. We know that a number is divisible by 9 if the sum of its digits is a multiple of 9. For m = 1 the number is 168 + 3171, the sum of whose digits is 9. Therefore, the required number is 171. Incorrect Answer: (b)171 Explanation: LCM (6, 7, 8) = 168 So the number is of the form 168m + 3 Now, 168m + 3 should be divisible by 9. We know that a number is divisible by 9 if the sum of its digits is a multiple of 9. For m = 1 the number is 168 + 3171, the sum of whose digits is 9. Therefore, the required number is 171.
#### 2. Question
Find the least number which when divided by 6,7,8 leaves a remainder of 3, but when divided by 9 leaves no remainder.
Answer: (b)171
Explanation:
LCM (6, 7, 8) = 168
So the number is of the form 168m + 3
Now, 168m + 3 should be divisible by 9.
We know that a number is divisible by 9 if the sum of its digits is a multiple of 9.
For m = 1 the number is 168 + 3171, the sum of whose digits is 9. Therefore, the required number is 171.
Answer: (b)171
Explanation:
LCM (6, 7, 8) = 168
So the number is of the form 168m + 3
Now, 168m + 3 should be divisible by 9.
We know that a number is divisible by 9 if the sum of its digits is a multiple of 9.
For m = 1 the number is 168 + 3171, the sum of whose digits is 9. Therefore, the required number is 171.
• Question 3 of 5 3. Question A rectangular field of dimension 180m 105m is to be paved by identical square tiles. Find the size of each tile and the number-of-tiles required. a) 15m15m, 84 b) 14m13m, 45 c) 13m13m, 96 d) 12m13m, 92 Correct Answer: (a) 15m15m, 84 Explanation: We need to find the size of a square tile such that a number of tiles cover the field exactly, leaving no area unpaved. For this, we find the HCF of the length and breadth of the field. HCF (180, 105) = 15 Therefore, size of each tile 15m x 15m Also, number of tiles = area of field / area of each tile Number of tiles (180 x 105)/(15 x 15) => Number of tiles = 84 Hence, we need 84 tiles, each of size 15m 15m Incorrect Answer: (a) 15m15m, 84 Explanation: We need to find the size of a square tile such that a number of tiles cover the field exactly, leaving no area unpaved. For this, we find the HCF of the length and breadth of the field. HCF (180, 105) = 15 Therefore, size of each tile 15m x 15m Also, number of tiles = area of field / area of each tile Number of tiles (180 x 105)/(15 x 15) => Number of tiles = 84 Hence, we need 84 tiles, each of size 15m * 15m
#### 3. Question
A rectangular field of dimension 180m * 105m is to be paved by identical square tiles. Find the size of each tile and the number-of-tiles required.
• a) 15m*15m, 84
• b) 14m*13m, 45
• c) 13m*13m, 96
• d) 12m*13m, 92
Answer: (a) 15m*15m, 84
Explanation:
We need to find the size of a square tile such that a number of tiles cover the field exactly, leaving no area unpaved.
For this, we find the HCF of the length and breadth of the field. HCF (180, 105) = 15 Therefore, size of each tile 15m x 15m Also, number of tiles = area of field / area of each tile Number of tiles (180 x 105)/(15 x 15) => Number of tiles = 84 Hence, we need 84 tiles, each of size 15m * 15m
Answer: (a) 15m*15m, 84
Explanation:
We need to find the size of a square tile such that a number of tiles cover the field exactly, leaving no area unpaved.
For this, we find the HCF of the length and breadth of the field. HCF (180, 105) = 15 Therefore, size of each tile 15m x 15m Also, number of tiles = area of field / area of each tile Number of tiles (180 x 105)/(15 x 15) => Number of tiles = 84 Hence, we need 84 tiles, each of size 15m * 15m
• Question 4 of 5 4. Question Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively. a) 1256 b) 1394 c) 1056 d) 956 Correct Answer: (b) 1394 Explanation: Here, (20-14)=6, (25-19)=6, (35-29)=6 and (40-34)=6 Required number =(L.C.M. of 20, 25, 35, 40)-6 Required number=1400-6-1394. Hence, option B is correct. Incorrect Answer: (b) 1394 Explanation: Here, (20-14)=6, (25-19)=6, (35-29)=6 and (40-34)=6 Required number =(L.C.M. of 20, 25, 35, 40)-6 Required number=1400-6-1394. Hence, option B is correct.
#### 4. Question
Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.
Answer: (b) 1394
Explanation:
Here, (20-14)=6, (25-19)=6, (35-29)=6 and (40-34)=6
Required number =(L.C.M. of 20, 25, 35, 40)-6
Required number=1400-6-1394.
Hence, option B is correct.
Answer: (b) 1394
Explanation:
Here, (20-14)=6, (25-19)=6, (35-29)=6 and (40-34)=6
Required number =(L.C.M. of 20, 25, 35, 40)-6
Required number=1400-6-1394.
Hence, option B is correct.
• Question 5 of 5 5. Question If a and b are positive integers, then what is HCF of (a/HCF of (a, b) , b/HCF of (a, b) ) equal to? a) a b) b c) 1 d) a/HCF(a, b) Correct Answer: (c)1 Explanation: Let the two positive numbers to be a=2, and b=3 Now on putting the respective values of a and b in the given equation, we get HCF of (2/HCF of (2,3) , 3/HCF of (2,3) ) HCF of (2/1 , 3/1) = HCF of (2,3) =1 Incorrect Answer: (c)1 Explanation: Let the two positive numbers to be a=2, and b=3 Now on putting the respective values of a and b in the given equation, we get HCF of (2/HCF of (2,3) , 3/HCF of (2,3) ) HCF of (2/1 , 3/1) = HCF of (2,3) =1
#### 5. Question
If a and b are positive integers, then what is
HCF of (a/HCF of (a, b) , b/HCF of (a, b) ) equal to?
• d) a/HCF(a, b)
Answer: (c)1
Explanation:
Let the two positive numbers to be a=2, and b=3
Now on putting the respective values of a and b in the given equation, we get
HCF of (2/HCF of (2,3) , 3/HCF of (2,3) )
HCF of (2/1 , 3/1) = HCF of (2,3) =1
Answer: (c)1
Explanation:
Let the two positive numbers to be a=2, and b=3
Now on putting the respective values of a and b in the given equation, we get
HCF of (2/HCF of (2,3) , 3/HCF of (2,3) )
HCF of (2/1 , 3/1) = HCF of (2,3) =1
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