## Tuesday, August 27, 2013

### Looking at More Complex GRE-style Quantitative Aptitude Questions

First, the answers from last time:

Verbal (I):

1. (B), 2. (C),  3. (D), 4. (E), 5, (B)

Verbal (II):

1. (C), 2. (A), 3. (B), 4. (E)

Verbal -Analytic (III):

1. (A), 2. (B), 3. (A), 4. (E), 5. (E), 6. (C)

We look now at GRE- style quantitative questions. In each case for the given question set, study the graph and information concerning it, then answer the questions that follow:

Quantitative (I): 7 Minutes:

The graph shown displays the chemical potential vs relative temperature for pure water, a saline solution and ice.  For  an "ideal solution" (a solution in which all molecules interact in the same way) the chemical potential of water in the solution is given by :

µsolution water = µpure water + RT ln xsolution water

where R is the gas law constant (8.314 J/mol K), T is the temperature, and xsolution water is the mole fraction of water in the solution. (On the graph, T0 is the freezing point of the pure water. ) As salt is added to the water, the concentration of water in the solution goes down. That makes xsolution water less than one, and the natural log of a number less than one is negative. That makes the concentration correction negative, so the chemical potential of water will drop as more salt is added.

1. The decrease in chemical potential occurs because:

A. The quantity x (solution water) is less than one.

B. There is a lower concentration of water in the solution than in the pure liquid.

C. There is a higher concentration of water in the solution than in the pure liquid.

D. There is no change in concentration between ice and pure liquid.

E.  The freezing point remains unchanged.

2. At the freezing point, it is clear that:

A. Ice and pure water co-exist

B. The tendency of the ice to melt is exactly counter balanced by the tendency of the water to freeze

C.  The chemical potentials must be equal so that: µice = µpure water

D.  Pure water has a higher chemical potential than water in salt solution

E. All of the above.

3. It is clear that when salt is mixed with the pure water solution:

A. The dissolved salt will lower the chemical potential of the (originally) pure water.

B.  The chemical potential of the ice is barely affected at all.

C. The water must now be more unstable than ice - so the ice will melt more slowly.

D.  Answers A, B and C

4. Which, if any, of the following can be deduced from the graph?

A. The chemical potential for all 3 substances rises as the temperature decreases.

B. The solution (water in) curve is shifted below the curve for pure water because the RT in the xsolution water   term is less than zero.

C. The lower chemical potential of solution water shifts the point of intersection (with that for ice) to the left. This means the freezing point for water in the solution is lower than the freezing point for the pure water.

E. Answers A, B and C.

Quantitative II: (8 Minutes)

The graph above shows the radiocarbon C-14 excess over C-12 over a 2,000 year period. In general, C14 is produced in the upper atmosphere via the impact –interaction with high energy cosmic rays, say from galactic sources. Solar activity in turn modulates the intensity of these cosmic rays via the action of the heliosphere's magnetic field which deflects a fraction of the intense cosmic ray flux and other harmful interstellar radiation.

When the Sun is more active, the heliosphere will be stronger, shielding the Earth from more intense cosmic rays the effect of which is to reduce the C14 produced in the Earth’s upper atmosphere. Conversely, when the Sun is less active then the shield is weaker and more intense cosmic rays penetrate to our upper atmosphere yielding more C14 produced.

To conform with observed solar activity the plot (from P.E. Damon :'The Solar Output and Its Variation', The University of Colorado Press, Boulder, 1977) is such that increasing radiocarbon (C14) is downward and indicated with (+). The deviations in parts per thousand are shown relative to an arbitrary 19th century reference level.

Questions:

1. The  increasing C14/C12 ratio, i.e. from left to right on the graph probably arises from:

(A) Injection of anthropogenic CO2 into the Earth's atmosphere.

(B) The result of the known, slow decrease in the strength of the Earth’s magnetic moment.

(C) Increased cosmic ray fluxes on Earth

(D) Increased radiocarbon production on Earth resulting from (C)

(E) All the above

2. The sharp upward spike at the modern end of the curve (e.g. from about 1850 on) , representing a marked drop in relative radiocarbon, is probably due to:

(A) Anthropogenic causes—the onset of increased population and the Industrial Age

(B) The burning of low radiocarbon fossil fuels, such as coal and oil

(C) The systematic burning off of the world’s forests for agriculture.

(D)  Processes (B) and (C) only

(E) All the processes: A, B and C

3. The percentage C14 excess over C 12 by the mid-20th century is approximately:

(A) +25,  (B) -25, (C) +30 (D) +5  (E) +10

The graph below shows the changes in the heliosphere's magnetic field over different solar cycles,  starting from 1900 to about the beginning of the 1st quarter of 2000.  The vertical axis gives the magnitude of the magnetic field (B) in nano-Tesla. Note that the red portion of the graph denotes magnitudes observed from Earth, while the earlier (blue, light green) denoted inferred magnitudes.

4. Based on where Damon's (earlier) C-14 excess over C12  graph terminates, estimate the magnitude of the inferred or observed heliospheric magnetic field:

(A) 3 nT  (B) 7 nT,  (C) 9 nT  (D) 5 nT  (E) 8 nT

5. According to existing solar data, sunspot cycle 16 was a "weak cycle"  which led to a much more energetic and active one (cycle 17). Estimate the ratio of the maximum magnitudes of the  heliospheric magnetic fields, in cycle 17 relative to 16:

(A) 0.5 (B) 2.0  (C) 8/7   (D) 8.5/6.8  (E) 9/ 7

6. According to the World Meteorological Office:

The year 2010 is almost certain to rank in the top three warmest years since the beginning of instrumental records in 1850.”

Assuming the validity of the arbitrary norm (zero line or abscissa) for 1890 in the Damon graph, then it is clear that the magnitude of the Middle Ages warming period (relative C14 strength of -18), for example, is less than about ½ the relative effect attributed mainly to anthropogenic sources in the modern era (-40).  Based on this, and examining the two graphs, is it logical to conclude that the magnitude of the heliosphere magnetic field directly affects climate change on Earth?

(A) No, not enough data  (B) Yes, to a small degree - because it modulates cosmic ray flux

(C) Yes, since the magnitude of the relative C14 over C12 excess, for Middle Ages warming, is less than about ½ the relative effect attributed mainly to anthropogenic sources in the modern era.

(D) No, because there weren't actual instruments to measure the heliosphere magnetic field  in the Middle Ages.

(E) Yes, because the maximum peak for cycle 23 falls close enough to the beginning of 2010.

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Answers tomorrow. Also, where do you stand on a truncated GRE aptitude test scale? Find out tomorrow, assuming you've taken all these sample segments in the time.

#### 1 comment:

kabita pal said...

Great man. Nice collection of quantitative aptitude questions. Hope it will help at my CTET exam.