In what year did the population of City X first exceed 1,000,000 ?

Question

(1) The population of City Y first exceeded 1,000,000 in 1963, and the population of City X first exceeded 1,000,000 41⁄2 years after the population of City Y first exceeded 1,000,000.

(2) The population of City Z first exceeded 1,000,000 in 1930, and the population of City X first exceeded 1,000,000 37 years after the population of City Z first exceeded 1,000,000.

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JerryAtDreamScore · Answer

Statement 1 Alone:

We don't know if Y exceeded the 1 million in the first half of the year or 2nd half of the year. So X could have exceeded 1 million in 1967 or 1968, then statement 1 is insufficient. (The fraction should be is  4\frac{1}{2}  according to statement 2).

Statement 2 Alone:

Supposedly they mean City X exceeds 1 million exactly 37 years after Z did, then the answer is in year 1967, so statement 2 is sufficient.

Answer: B

sanjitscorps18 · Answer

(1) The population of City Y first exceeded 1,000,000 in 1963, and the population of City X first exceeded 1,000,000 41⁄2 years after the population of City Y first exceeded 1,000,000.

Lets add 4 years to 1963 we have the year 1967. Now we have to deal with the 6 months. If the instant of population of Y exceeding 1,000,000 was before June then the population of X exceeded 1,000,000 in the same year.
Else the population of X exceeded in the next year i.e. 1968

For e.g. we have the below situations 
1. Y exceeded the population of 1,000,000 in April 1963 then X exceeded the population of 1,000,000 in April,1967 + 6 months = October 1967
2. Y exceeded the population of 1,000,000 in September 1963 then X exceeded the population of 1,000,000 in September 1967 + 6 months = March 1968.
Hence the year can be 1967 or 1968
Insufficient

(2) The population of City Z first exceeded 1,000,000 in 1930, and the population of City X first exceeded 1,000,000 37 years after the population of City Z first exceeded 1,000,000.
In this scenario the year and months correlate hence there is a clear demarcation of the time when the population of City X crossed 1,000,000. 
Sufficient

Option B

gemministorm · Answer

I do not understand,
1963+4.5=1967.5. Without knowing the month in 1963, 4.5 years later could fall in 1967 or 1968 -- but be it 1967.4 or 1967.6 it's still year 1967 isn't it? only on 1st Jan 1968 post new year, will the year be 1968 no?

Bunuel · Answer

If Y crossed early in 1963, X would in 1967. However, if late in 1963, X would in 1968. Hence, the exact year can’t be fixed.

gemministorm · Answer

aha,
- If Y crossed in February 1963, then 1963 + 4.5 years → August 1967 (year 1967).
- if Y crossed in November 1963, then 1963 + 4.5 years → May 1968 (year 1968).

In what year did the population of City X first exceed 1,000,000 ?

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GMAT Data Sufficiency (DS) Questions

In what year did the population of City X first exceed 1,000,000 ?

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