x divides \(\left ( \left ( 49 \right )^{15} -1\right )\) completely. What is \(x\) ?
Answer: A
\(\left (x^{n}-1 \right )\) is divisible by \(x+1\) if \(x\) is an even number.
\(\left ( \left ( 49 \right )^{15} -1\right )\) =\(\left ( \left ( 7^{2} \right )^{15} -1\right )\) =\(\left ( 7 \right )^{30} -1\)
which is divisible by \(7+1\), \(8\)
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The sum of three consecutive integers is 102. Find the lowest of the three?
Answer: D
Three consecutive numbers can be taken as \((P - 1), P, (P + 1)\)
So, \((P - 1) + P + (P + 1) = 102\)
\(3P = 102 => P = 34\)
The lowest of the three \(= (P - 1) = 34 - 1 = 33\)
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\((112 \times 5^{4}) = ?\)
Answer: B
\((112 \times 5^{4})\\= 112 \times \left ( 10\div 2 \right )^{4}\\= \dfrac{112\times 10^{4}}{2^{4}}\\= \dfrac{1120000}{16}\\ = 70000\)
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\((935421 \times 625) = ?\)
Answer: B
\(935421 \times 625\\ = 935421 \times 5^{4}\\ =935421 \times \left ( \dfrac{10}{2} \right )^{4}\\ =\dfrac{935421 \times 10^{4}}{2^{4}}\\ =\dfrac{9354210000}{16}\\ =584638125\)
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When writing numbers from 1 to 10,000, how many times is the digit 9 written ?
Answer: C
The digits 9 occurs in the thousands place in 1000 numbers.
It occurs in the hundreds place in 1000 numbers and so on
The digit occurs 4000 times.
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The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes \(\dfrac{3}{4}\). Find the original fraction?
Answer: C
The denominator be \(P\), the numerator will be \((P - 8)\)
The fraction will be \(\dfrac{(P - 8)}{P}\)
Adding 3 to the numerator and subtracting 3 from the denominator,
\(\dfrac{(P - 8 + 3)}{P - 3}= \dfrac{3}{4}\)
\(\dfrac{(P - 5)}{P - 3}= \dfrac{3}{4}\)
\(P = 20 - 9 \Rightarrow P = 11\)
The fraction is: \(\dfrac{3}{11}\)
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a,b,c,d and e are five consecutive numbers in increasing order of size. Deleting one number from the set decreased the sum of the remaining numbers in the set by 20%.
Which one of the following numbers was deleted?
Answer: C
No answer description available for this question.
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What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Answer: A
\(\dfrac{1056}{23}=45.91\\ 23 \times 45=1035\\ 1056-1035=21\\ \therefore 23-21=2\)
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The remainder when the positive integer m is divided by 7 is x. The remainder when m is divided by 14 is x+7.
Which one of the following could m equal?
Answer: B
No answer description available for this question.
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The difference between the local value and face value of 7 in the numeral 657903 is:
Answer: B
\((Local value)-(Face value)\\= (7000-7)\\=6993\)
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