Number System
- A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively.
When it is successively divided by 5 and 4 the respective remainders will be
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According to question ,
The least number X in this case will be determined as follows:
Y = 5 × 1 + 4 = 9
X = 4 × Y + 1 = 4 × 9 + 1 = 37
Now,Correct Option: C
According to question ,
The least number X in this case will be determined as follows:
Y = 5 × 1 + 4 = 9
X = 4 × Y + 1 = 4 × 9 + 1 = 37
Now,
Hence, the respective remainders are 2, 3.
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If 3 of the difference of 2 1 and 1 2 is subtracted from 2 4 4 3 3 of 3 1 the result is 4
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According to question , we have
13 × 2 − 
9 − 5 
× 3 4 3 4 3 4 Required answer = 13 − 27 − 20 × 3 6 12 4
Correct Option: D
According to question , we have
13 × 2 − 9 − 5 × 3 4 3 4 3 4 Required answer = 13 − 27 − 20 × 3 6 12 4 Required answer = 13 − 7 × 3 = 13 − 7 6 12 4 6 16 Hence Required answer = 104 − 21 = 83 48 48
- Solve the below equation.
1 0.04
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On Replacing the decimal in given number , we can write it
1 = 100 0.04 4
Correct Option: D
On Replacing the decimal in given number , we can write it
1 = 100 = 25 0.04 4
- A number of friends decided to go on a picnic and planned to spend ₹108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute ₹3 extra. The number of them who attended the picnic was :
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Let the original number of friends be x.
∴ 108 + 108 = 3 x − 3 x ⇒ 108 x − x + 3 
= 3 x(x − 3)
⇒ x (x – 3) = 108
⇒ x2 – 3x – 108 = 0
⇒ x2 –12 x + 9x –108 = 0
⇒ (x– 12) + 9 (x – 12) = 0
⇒ (x – 12) (x + 9) = 0
⇒ x = 12 as x ≠ – 9
∴ The number of friends who attended the picnic
= 12 – 3 = 9Correct Option: C
Let the original number of friends be x.
∴ 108 + 108 = 3 x − 3 x ⇒ 108 x − x + 3 = 3 x(x − 3)
⇒ x (x – 3) = 108
⇒ x2 – 3x – 108 = 0
⇒ x2 –12 x + 9x –108 = 0
⇒ (x– 12) + 9 (x – 12) = 0
⇒ (x – 12) (x + 9) = 0
⇒ x = 12 as x ≠ – 9
∴ The number of friends who attended the picnic
= 12 – 3 = 9
- If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is :
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Let the number be x.
∴ According to question,
2x + 20 = 8x – 4
or 8x – 2x = 20 + 4
or 6x = 24
∴ x = 4Correct Option: C
Let the number be x.
∴ According to question,
2x + 20 = 8x – 4
or 8x – 2x = 20 + 4
or 6x = 24
∴ x = 4
