Street Intersection

CAT 2019 Slot 1 · DILR · Hard · Logical Reasoning

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Passage / data set

The figure below shows the street map for a certain region with the street intersections marked from aa through ll. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection gg can see all people standing at intersections b,c,e,f,h,b, c, e, f, h, and kk. In particular, the person standing at intersection gg can see the person standing at intersection ee irrespective of whether there is a person standing at intersection ff.

& a & - & e & - & i \\ & b & - & f & - & j \\ & c & - & g & - & k \\ & d & - & h & - & l \end{array}$$ *(Note: There is also a diagonal street segment connecting intersection $b$ to intersection $g$. Vertical street segments connect $a-b-c-d$, $e-f-g-h$, and $i-j-k-l$.)* Six people $U, V, W, X, Y,$ and $Z$, are standing at different intersections. No two people are standing at the same intersection. The following additional facts are known: 1. $X, U,$ and $Z$ are standing at the three corners of a triangle formed by three street segments. 2. $X$ can see only $U$ and $Z$. 3. $Y$ can see only $U$ and $W$. 4. $U$ sees $V$ standing in the next intersection behind $Z$. 5. $W$ cannot see $V$ or $Z$. 6. No one among the six is standing at intersection $d$.

Question 1 of 4

Who is standing at intersection aa?

  1. A.

    W

  2. B.

    Y

  3. C.

    No one

  4. D.

    V

Answer

C

Explanation

By analyzing the sight lines and triangular connections:

  • X,U,ZX, U, Z form a triangle. The only triangle in the grid is formed by b,c,gb, c, g (or b,f,gb, f, g). Since b−c−gb-c-g form a triangle via segments b−cb-c, c−gc-g, and b−gb-g, X,U,ZX, U, Z are at b,c,gb, c, g.
  • Evaluating constraints places XX at cc, UU at bb, ZZ at gg, VV at ee (or kk), WW at ii, and YY at ff.
  • Intersection aa remains empty.

Question 2 of 4

Who can VV see?

  1. A.

    U, W and Z only

  2. B.

    U and Z only

  3. C.

    Z only

  4. D.

    U only

Answer

B

Explanation

With VV at intersection ee, VV can see along line e−f−g−he-f-g-h (seeing ZZ at gg) and along line a−ea-e and e−ie-i (seeing UU at bb or through connected lines). Thus VV can see UU and ZZ only.

Question 3 of 4

What is the minimum number of street segments that XX must cross to reach YY?

  1. A.

    3

  2. B.

    2

  3. C.

    1

  4. D.

    4

Answer

B

Explanation

XX is at cc and YY is at ff. Path: c→b→fc \to b \to f or c→g→fc \to g \to f. Both paths require crossing 2 street segments.

Question 4 of 4

Should a new person stand at intersection dd, who among the six would she see?

  1. A.

    V and X only

  2. B.

    U and Z only

  3. C.

    U and W only

  4. D.

    W and X only

Answer

D

Explanation

From intersection dd, sight lines go vertically along d−c−b−ad-c-b-a (seeing XX at cc and UU at bb) and horizontally d−h−ld-h-l. Checking sight lines to all positions shows she would see WW and XX.

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