Data Sufficiency Practice Test Questions - Verbal Reasoning

13 boys and 26 girls are in the ratio 1:2.
Statement a has 3 boys and 6 girls, also in the ratio 1:2, with 9 workers in total taking 26 days. Since 13 + 26 = 39 workers is the same mix scaled up (39/9 times as many workers of the same 1:2 composition), the time scales down in the same proportion: 26 × (9/39) = 6 days. So statement a alone is sufficient.
Statement b has boys:girls = 4:4 = 1:1, which does not match the required 1:2 ratio, so it cannot be used to find the combined rate for a 1:2 mix.
Statement c has boys:girls = 12:20 = 3:5, which also does not match 1:2, so it is not sufficient either.
Only statement a is sufficient.

From (a), if the bike's length is L and speed is s, then L/s = 13 seconds. From (b), crossing a platform of length x means (L + x)/s = y minutes. Together, these are two equations in the two unknowns L and s, which can be solved to find s. Neither (a) nor (b) alone is sufficient, but together they are. Statement (c) alone (crossing another moving bike) does not give the bike's own speed without knowing the other bike's speed. Hence, "Only a & b" is sufficient.

From (c): the middle number is 33.33% (1/3) greater than the first, so First : Middle = 3 : 4; and 33.33% less than the third, so Middle : Third = 2 : 3. Combined: First : Middle : Third = 3 : 4 : 6, which gives the exact same ratio Middle : Third = 2 : 3 stated directly in (b). So either (b) or (c) gives the ratio among the three numbers, and combined with the total from (a), the absolute values (and hence the second number) can be found. Hence, "Either a and b or a and c" is sufficient.

To find the number of articles sold from the total profit, the profit per article (selling price minus cost price) is needed. None of the statements give the cost price per article -- (a) gives only total profit, (b) gives marked price (not necessarily the selling price), and (c) gives selling price but not cost price. No combination of these lets the profit per article be found, so the number of articles sold cannot be determined; hence "None of these".

Statement A: SI=Prt/100 gives 3600=15000xrx2/100, so r=12% -- a definite answer. Statement B does not specify the time period over which the Rs.216 difference applies, so the standard 2-year CI-SI difference formula cannot be applied with confidence, leaving B alone insufficient.

Statement A gives digits 4 and 7 (product 28, difference 3), but the number could be 47 or 74 -- ambiguous alone. Statement B alone (units < tens) has no concrete digits. Combined: units < tens means the number is 74.

Statement A introduces a third unrelated unknown (Sugandha) with no concrete value, giving no help alone. Statement B: with Neera=2k, Shalu=k, (2k+4)/(k+4)=3/2 gives k=4, so Shalu is 4 -- sufficient alone.

Statement A: 10xCP=8x250 gives CP=200, so profit=50 -- sufficient alone. Statement B: 25% profit at SP=250 gives CP=250/1.25=200, so profit=50 -- also sufficient alone. Either statement alone suffices.

Total of all 6 = 150,000. Combining both statements gives C+E+G+H=112,000, so A+J=38,000 -- but this only pins down the combined total of A and J, not A individually. Even both statements together are not sufficient; more data is needed.

From the two means, Mon+Tue+Wed=111 and Tue+Wed+Thu=102, giving Mon-Thu=9 -- already derivable without any statement, so statement III adds nothing new. Statement I (Thu=4/5 Mon) combined with Mon-Thu=9 gives Mon=45, Thu=36. Statement II (Mon+Thu=81) combined with Mon-Thu=9 also gives Thu=36. Either I or II alone suffices.

Statements II and III both reduce to the same ratio (Bigger = 4/3 × Smaller), so they are not independent of each other and combining just II and III gives no new information.
Statement I alone (Bigger - Smaller = 6) is one equation with two unknowns, so it is not sufficient by itself either.
But statement I together with either II or III gives two independent equations: Bigger - Smaller = 6 and Bigger = 4/3 × Smaller.
Solving: 4/3 × Smaller - Smaller = 6, so Smaller/3 = 6, Smaller = 18 and Bigger = 24. Sum = 42.

Statement I is always true for simple interest regardless of principal or rate (SI is proportional to time), so it gives no new information. Statements II and III together give Amount=P(1+rt/100): 750=Px1.4, so P~535.71.

From I: A+B+D=60. From II: C+D=50. Combined with the total 96: D=110-96=14, so A+B=46 and C=36 -- but A and B remain combined (A+B=46), never individually separated. Even both statements together do not determine B alone.

Combining both statements still leaves Philosophy expressed in terms of an unresolved free variable, since neither statement pins down an absolute individual value -- the system remains underdetermined even together.

Statement II alone gives the labeled price (2000=1.25xLabeled, so Labeled=1600). Statement I alone gives only a percentage, no absolute value. Combined: Richard's cost = 80% x 1600 = 1280.

B's rate=1/12 (given). Statement I gives A's rate (1/3-1/12=1/4). Statement II gives C's rate (1/6-1/12=1/12). Both are needed to get A+B+C=1/4+1/12+1/12=5/12, i.e. 2.4 days.

Neither statement alone pins down all three bags (each leaves 2 unknowns among 3). Combined: I=III+5, II=I/2, and I+II+III=10 gives I=6, II=3, III=1, satisfying all conditions.

A "bundled offer" typically implies a discount versus the sum of individual prices, so the bundle price minus the laptop's standalone price does not necessarily equal the printer's standalone price -- without knowing the discount, the printer's individual price cannot be determined even from both statements together.