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. 13 boys and 26 girls are the same group taken 13/3 times, so the time is 26 × 3/13 = 6 days. So statement a alone is sufficient.
Statement b has boys:girls = 1:1, which does not match the 1:2 mix. It gives only one equation in the two unknown rates, so it is not sufficient.
Statement c is also a 1:1 mix (twice the group in b, finishing in half the time), so it repeats the information in b and is not sufficient, alone or with b.
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.

Let H, E, S and P be his marks. H = (H + E + S + P)/4 + 15, so 3H = E + S + P + 60.
Statement I gives H + P = 12 and statement II gives S - E = 120.
That is three equations in four unknowns, so P cannot be found even with both statements.

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.

I alone says nothing about M, and II alone says nothing about D. Together: N is a daughter of D, and M's father has only two daughters, N and P. M is not one of them, so M is a son, and M is N's brother. Hence M is D's son. So, both statements together are needed.

From I, K is the son of L's daughter, so K is L's grandson. II only gives the number of grandchildren and does not say who K is. So, statement I alone is sufficient.

Each statement gives one distance from Town B, but the directions are not given, so the positions of A and C relative to each other are unknown. The distance between A and C cannot be found even from both statements together. So, even both statements together are not sufficient.

Each statement alone gives the position of only one house. Together, the two houses lie on a straight north-south line on opposite sides of the school, so they are 2 + 2 = 4 km apart. So, both statements together are needed.

Together, R is Q's daughter and P's sister, so P is Q's child. But P's gender is not given, so we cannot say whether P is Q's son or daughter. Neither statement alone helps either. So, even both statements together are not sufficient.

I alone does not mention Y, and II alone does not link X to Z. Together, X is Z's sister and Z is Y's son, and X is a girl, so X is Y's daughter. So, both statements together are needed.

From I, R > Q > P and S, so R is the tallest. From II, Q and R are both taller than P and S, but we cannot tell which of Q and R is taller. So, statement I alone is sufficient.

II directly says that D scored more than everyone else, so D is the highest. I compares B with A and C only and says nothing about D. So, statement II alone is sufficient.

From II, Sohan + Mohan + Kiran = 48 and Kiran = Sohan + Mohan, so Sohan + Mohan = 24. II alone does not mention Rohan, and I alone gives no age. Together, Sohan = Mohan = Rohan, so Rohan = 24 ÷ 2 = 12 years. So, both statements together are needed.

From I, Meera's age = 40 ÷ 2 + 4 = 24 years. From II, Meera's age = 2 × 12 = 24 years. Each statement alone gives the answer. So, either statement alone is sufficient.

From I, the word common to 'fresh water' and 'cold water please' is 'water', and the common digit is 7, so 7 = water and 2 = fresh. From II, the word common to 'fresh water' and 'fruit is fresh' is 'fresh', and the common digit is 2, so 2 = fresh and 7 = water. Each statement alone is enough. So, either statement alone is sufficient.

From I, the word common to 'bright sun' and 'good bright day' is 'bright', and the common digit is 1, so 1 = bright and 8 = sun. II has no word or digit in common with '81', so it does not help. So, statement I alone is sufficient.

Together, Ajay + Bina = (C − 12) + (C + 8) = 2C − 4, where C is the number Chetan has. Since C is not known, the total cannot be found even from both statements. So, even both statements together are not sufficient.

Each statement alone relates the two earnings but gives no amount. Together: 2S = S + 5,000, so S = Rs. 5,000 and Ravi earns Rs. 10,000. Total = Rs. 15,000. So, both statements together are needed.

I alone leaves R and S unplaced, and II alone leaves P and Q unplaced. Together, T finished after Q, P, R and S, so T finished last. So, both statements together are needed.

II directly says that D reached before everyone else. I shows that D came before A, B and C, but it says nothing about E. So, statement II alone is sufficient.

From I, Y is older than Z alone, so Z is the youngest. From II, W is the oldest and X is second, but Y and Z cannot be ordered. So, statement I alone is sufficient.

II directly says that Pooja is the shortest. I tells us only that Amit is the tallest and Ravi is second. So, statement II alone is sufficient.

From I, (y − 2)(y − 3) = 0, so y = 2 or 3. II alone allows any odd number. Together, y = 3. So, both statements together are needed.

From II, n = 7. From I, n could be 7 or −7, so I alone is not enough. So, statement II alone is sufficient.

From II, the total weight = 2 × 48 = 96 kg. I gives only the difference between the weights, not the total. So, statement II alone is sufficient.

From I, the numbers are 20 and 14, so the sum is 34. From II, the numbers could be 20 and 14, 28 and 10, 35 and 8, and so on, so the sum is not fixed. So, statement I alone is sufficient.

From I, (p − 4)² = 0, so p = 4. II allows any positive even number. So, statement I alone is sufficient.

From II, (k + 3)² = 0, so k = −3. From I, k could be 3 or −3, so I alone is not enough. So, statement II alone is sufficient.

From II, the triangle has a right angle, so it cannot be equilateral (all angles of an equilateral triangle are 60°); the answer is "No". From I, the triangle is isosceles, but it may or may not be equilateral. So, statement II alone is sufficient.

I alone makes ABCD a rhombus, which need not be a square. II alone fits many shapes. Together, a rhombus with a right angle has all its angles equal to 90°, so ABCD is a square. So, both statements together are needed.

From I, 3a = 15, so a = 5. II allows any prime number. So, statement I alone is sufficient.

From I, 2b = 12, so b = 6. From II, b = 6. Each statement alone gives the value. So, either statement alone is sufficient.

Each statement gives the price of only one item. Together, the total = 40 + 60 = Rs. 100. So, both statements together are needed.

From I, the trousers cost 800 + 400 = Rs. 1,200, so the total = 800 + 1,200 = Rs. 2,000. II gives only the ratio of the prices, not the amounts. So, statement I alone is sufficient.

From I, two adjacent sides of the rectangle are equal, so all four sides are equal and it is a square. II is true for every rectangle, so it does not help. So, statement I alone is sufficient.

From II, a parallelogram with all sides equal is a rhombus. I is true of every parallelogram, so it does not help. So, statement II alone is sufficient.

The angles of a triangle add up to 180°, so two angles are needed. Together, C = 180° − 50° − 70° = 60°. So, both statements together are needed.

From I, all three angles of an equilateral triangle are equal, so each is 60°. II gives only one angle; the other two can vary. So, statement I alone is sufficient.

I gives only the number of girls, and II gives only a ratio. Together, boys = 24 × 5 ÷ 6 = 20, so there are 20 + 24 = 44 students. So, both statements together are needed.

From I, total = 18 ÷ 0.3 = 60. From II, total = 42 ÷ 0.7 = 60. Each statement alone gives the answer. So, either statement alone is sufficient.