Directions: Pick the correct options from the given alternatives 10 : 729 :: 7 : ?
216
A number analogy works like an equation: first find the precise operation that turns the first number of a pair into the second, then perform that identical operation on the new number.
Examine the given pair 10 : 729. The value 729 is a familiar perfect cube, because \(9\times9\times9=9^{3}=729\), so a cube is clearly involved.
The cube root here is 9, and 9 is exactly one less than the starting number 10. The rule therefore is: reduce the number by 1 and cube the result, that is \((10-1)^{3}=9^{3}=729\).
Before trusting the rule, note it must be a genuine relationship and not a coincidence; the neat 'subtract 1, then cube' structure makes it the natural pattern.
Now apply the same rule to 7. Subtracting 1 gives 6, and the operation calls for cubing that.
Cubing gives \((7-1)^{3}=6^{3}=6\times6\times6=216\), which matches one of the offered choices.
Hence the number that replaces the question mark is 216.
Similar Questions
Select the option that is related to the fifth letter-number cluster in the same way as the second letter-number cluster is related to the first letter-number cluster and fourth letter-number cluster is related to third letter-number cluster.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g.13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
OP8 : IJ66 :: FN19 : ZH363 :: AW13 : ?
Select the option which is related to the fifth term in the same way as the second term is related to the first term and the fourth term is related to the third term.
IGEC : DFHJ : : USQO : PRTV : : NLJH : ?
In each of the following question, there is a certain relationship between two given numbers on one side of (::) and one number is given on another side of (::) where another number is to be found from the given alternatives, having the same relationship with this number as the numbers of the given pair bear. Choose the best alternative.
4 : 64 :: 5 : ?
Directions: Choose the related word from the given alternatives
Resistance : ? :: Magnetic flux : Weber
Directions: Pick the correct options from the given alternatives
GERMAN :NAMREG :: INDONESIA :?
Directions: Select the related letter from the given alternatives
RATS: STAR :: YXALG : ?
Directions: Select the related letter from the given alternatives
MARIGOLD: DMARIGOL:: JASMINE :?
Directions: Pick the correct options from the given alternatives
201 : 423 :: 501 : ?
Directions: Select the related word from the given alternatives
Sleepy: Drowsy:: Anger: ?
Direction: Choose the correct options from the alternative
52 :27 :: 62 : ?
Important Questions from Analogy
Select the option that is related to the third term in the same way as the second term is related to the first term.
Day: Night :: Morning : ?Select the option that is related to the third term in the same way as the second term is related to the first term.
India : Country :: Delhi : ..........Select the option that is related to the third term in the same way as the second term is related to the first term.
MATE: NATE :: FATE: ?Select the option that is related to the third term in the same way as the second term is related to the first term.
13 : 196 :: 9 : .......
Select the related word pair from the given alternatives. Afghanistan : Kabul :: ....... : .........
